UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Towards an understanding of Aztec architecture and urban planning García Ocampo Rivera, Antonieta María de la Paz 2016

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
24-ubc_2016_may_garciaocamporivera_antonietamariadelapaz.pdf [ 33.42MB ]
Metadata
JSON: 24-1.0228255.json
JSON-LD: 24-1.0228255-ld.json
RDF/XML (Pretty): 24-1.0228255-rdf.xml
RDF/JSON: 24-1.0228255-rdf.json
Turtle: 24-1.0228255-turtle.txt
N-Triples: 24-1.0228255-rdf-ntriples.txt
Original Record: 24-1.0228255-source.json
Full Text
24-1.0228255-fulltext.txt
Citation
24-1.0228255.ris

Full Text

  TOWARDS AN UNDERSTANDING OF  AZTEC ARCHITECTURE AND URBAN PLANNING  by  Antonieta María de la Paz García Ocampo Rivera  B.Arch., Universidad Iberoamericana, 1990 M.A.S.A., The University of British Columbia, 1998  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES  (Interdisciplinary Studies)  [Architecture / Landscape Architecture / Archaeology]  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  March 2016  © Antonieta María de la Paz García Ocampo Rivera, 2016 ii  Abstract  There exists a vast literature examining every aspect of Aztec culture. Despite this, few studies focus specifically on Aztec architecture and its implications for understanding broader aspects of Aztec cosmology. This dissertation contributes to our knowledge of Aztec society through an exploration of architectural and urban design principles that guided the building of their cities and ceremonial precincts.  By examining ethnohistoric and archaeological sources, and drawing on evidence from several disciplines—art, astronomy, geography, geometry, mathematics and religion—I compile a body of information relevant to the study of Aztec architecture and urban planning. Cosmovision studies offer an understanding of ritual space and time; pictorial manuscripts contribute mathematical insights; analyses of monumental sculpture provide geometric knowledge; and high mountain archaeological research highlight the sacred landscape. The resulting information was then used in a set of archaeoastronomical analyses of seven pre-Aztec and Aztec architectural complexes. This approach builds on previous studies that have revealed the importance of astronomical considerations in Mesoamerican settlements.  In order to analyse Aztec ceremonial architecture and urban planning from an archaeoastronomical perspective, I developed a methodology that allowed accurate analyses of the astronomical and topographic orientations of settlements and ceremonial architecture. This methodology integrates a wide range of digital applications including Google Earth, Google Maps, solar charting, topographic analysis, open-content collaborative, geo-location-oriented photo sharing applications as well as a custom-built geometric application.  The results allow for a new understanding of: (1) the design principles of the Huey Teocalli, the unique Aztec double-temple architectural type found in almost all of their ceremonial centres, (2) the layout and design principles utilized in the construction of Tenochtitlan and Tlatelolco and, (3) the Aztec remodelling of Tenayuca, Santa Cecilia Acatitlan and Teopanzolco. These analyses are also extended to the antecedent cultures of the region, revealing new aspects of the urban design principles of Teotihuacan and Tula including an additional interpretation of the Tlaloc mural in Teotihuacan.  The implications of this research extend beyond Aztec scholarship, providing a replicable methodology that can be applied to the archaeoastronomical analysis of ancient settlements and ceremonial structures anywhere in the world. iii  Preface  This dissertation is original, unpublished, independent work by the author, Antonieta María de la Paz García Ocampo Rivera.  Permission for use in this dissertation of photographs, images, illustrations and visual excerpts from archival documents collected from the Hathi Trust Digital Library, the Biblioteca Digital Hispánica, the Dipòsit Digital de Documents de la Universitat Autònoma de Barcelona, the Gallica-bibliothèque numérique de la Bibliothèque Nationale de France, the Biblioteca Medicea Laurenziana, the digital map of Mexico City at the Uppsala University Library, the Foundation for the Advancement of Mesoamerican Studies, the Biblioteca Digital Mexicana, the Codices del INAH, Amoxcalli and the Mapas, Planos e Ilustraciones from the Archivo General de la Nación, granted by a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) license. Permission to use photographs from Wikipedia, Panoramio and Flickr granted by Creative Commons Attribution 4.0 International (CC BY 4.0) unless otherwise noted. Permission to use diagrams from Latin American Antiquity granted by a Copyright Clearance Center license. iv  Table of Contents  Abstract .......................................................................................................................................... ii Preface ........................................................................................................................................... iii Table of Contents ......................................................................................................................... iv List of Tables ................................................................................................................................ ix List of Figures .................................................................................................................................x Acknowledgements ................................................................................................................ xxxiv Dedication ............................................................................................................................... xxxvi Chapter 1: Introduction ................................................................................................................1 Chapter 2: Sources for the Study of Aztec Architecture and Urban Planning ......................14 2.1 Introduction ...................................................................................................... 14 2.2 Overview of Aztec Historiography .................................................................. 14 2.3 Pictorial Manuscripts ....................................................................................... 27 2.3.1 Codex Aubin ................................................................................. 28 2.3.2 Codex Azcatitlan ........................................................................... 30 2.3.3 Codex Borbonicus ......................................................................... 31 2.3.4 Codex Borgia ................................................................................ 32 2.3.5 Codex Boturini .............................................................................. 34 2.3.6 Codex Ixtlilxochitl ........................................................................ 35 2.3.7 Codex Magliabechiano ................................................................. 36 2.3.8 Codex Telleriano-Remensis .......................................................... 37 2.3.9 Codex Xolotl ................................................................................. 39 2.3.10 Historia Tolteca-Chichimeca ........................................................ 41 2.3.11 Mapa de Cuauhtinchan No. 2........................................................ 43 2.3.12 Mapa Quinatzin ............................................................................. 45 2.3.13 Summary of Architectural and Urban Depictions in Pictorial Manuscripts ................................................................................... 46 2.4 Pictorial Administrative Manuscripts .............................................................. 49 2.4.1 Codex Mendoza ............................................................................ 50 2.4.2 Codex of the Marquesado del Valle.............................................. 52 v  2.4.3 Plan and Title of a Property in Tenochtitlan ................................. 53 2.4.4 Codex Vergara .............................................................................. 54 2.4.5 Codex Santa María Asunción ....................................................... 56 2.4.6 Oztoticpac Lands Map .................................................................. 56 2.4.7 Summary of Architectural and Urban Depictions in Pictorial-Administrative Manuscripts .......................................................... 58 2.5 Eyewitness Accounts by the Conquistadores ................................................... 58 2.5.1 Hernán Cortes ............................................................................... 59 2.5.1.1 Description .......................................................................... 59 2.5.1.2 Summary of Architectural and Urban Depictions ............... 59 2.5.2 Bernal Díaz del Castillo ................................................................ 61 2.5.2.1 Description .......................................................................... 61 2.5.2.2 Summary of Architectural and Urban Depictions ............... 61 2.6 Chronicles Compiled by the Missionaries ....................................................... 62 2.6.1 Fray Bernardino de Sahagún ......................................................... 63 2.6.1.1 Description .......................................................................... 63 2.6.1.2 Summary of Architectural and Urban Depictions ............... 64 2.6.2 Fray Diego Durán ......................................................................... 67 2.6.2.1 Description .......................................................................... 67 2.6.2.2 Summary of Architectural and Urban Depictions ............... 67 2.7 Archaeological Evidence ................................................................................. 68 2.8 Monumental Sculpture ..................................................................................... 72 2.9 Urban and Architectural Models ...................................................................... 74 2.10 Oral History ...................................................................................................... 79 2.11 Chapter Summary............................................................................................. 79 Chapter 3: Aztec Typology .........................................................................................................80 3.1 Introduction ...................................................................................................... 80 3.2 Aztec Typology ................................................................................................ 80 3.3 Aztec Building Types ....................................................................................... 83 3.3.1 Single Temple Teocalli ................................................................. 85 3.3.2 Double Temple (or Twin Temple) Teocalli .................................. 87 vi  3.3.3 Circular Base Teocalli................................................................... 89 3.3.4 Warriors / Priests Precinct ............................................................ 91 3.3.5 Tzompantli .................................................................................... 93 3.3.6 Tlatchtli ......................................................................................... 95 3.3.7 Momoztli ....................................................................................... 97 3.3.8 Central Momoztli .......................................................................... 99 3.3.9 Quauhxicalli and Temalacatl ...................................................... 101 3.3.10 Calmecac ..................................................................................... 103 3.3.11 Coatepantli of Huey Teocalli and Perimeter Wall of Ceremonial Precinct .................................................................... 105 3.3.12 Nobility Dwellings: Calli and Tecpan ........................................ 107 3.3.13 Commoners Dwellings: Calli ...................................................... 109 3.3.14 Temazcalli ................................................................................... 111 3.3.15 Gardens and pools ....................................................................... 113 3.3.16 Markets ....................................................................................... 115 3.3.17 Engineering Works - Chinampa, Dams, Embankments, Dykes, Roads, Piers, Canals, and Bridges .................................. 117 3.4 Aztec Urban Forms ........................................................................................ 121 3.5 Chapter Summary........................................................................................... 123 Chapter 4: The Aztec Cosmological Concept of Space and Time .........................................124 4.1 Introduction .................................................................................................... 124 4.2 The Concept of Cosmovision ......................................................................... 124 4.3 The Conception of Space in Aztec Cosmology and Mythology .................... 125 4.4 The Coordination of Space and Time in the Aztec Calendar......................... 132 4.5 The Sacred Landscape.................................................................................... 136 4.6 High-Mountain Archaeology ......................................................................... 139 4.7 Chapter Summary........................................................................................... 142 Chapter 5: Aztec Concepts of Astronomy, Mathematics and Geometry .............................143 5.1 Introduction .................................................................................................... 143 5.2 Archaeoastronomy and Aztec Astronomy ..................................................... 143 5.2.1 Aztec Astronomy ........................................................................ 147 vii  5.2.2 Charting the Movement of the Sun ............................................. 154 5.3 Aztec Mathematics ......................................................................................... 157 5.3.1 Linear Measuring System ........................................................... 160 5.3.2 Angular Measuring System......................................................... 165 5.4 Aztec Geometry ............................................................................................. 167 5.4.1 Geometric Figures in Aztec Design ............................................ 170 5.4.1.1 Circle ................................................................................. 170 5.4.1.2 Polygons ............................................................................ 171 5.4.1.3 Triangles ............................................................................ 172 5.4.1.4 Square and Rectangles ...................................................... 173 5.5 Aztec Building Practice.................................................................................. 178 5.5.1 Construction Trades and Architect ............................................. 181 5.5.2 Construction Materials ................................................................ 186 5.5.3 Construction Tools ...................................................................... 187 5.6 Chapter Summary........................................................................................... 190 Chapter 6: Archaeoastronomical Analyses of Selected Pre-Aztec and Aztec Sites .............192 6.1 Introduction .................................................................................................... 192 6.2 Methodology .................................................................................................. 193 6.3 Methodological Steps for the Digital Topographic and Archaeoastronomical Analyses ...................................................................... 203 6.4 Archaeoastronomical Analyses of Selected Pre-Aztec Sites ......................... 234 6.4.1 TEOTIHUACAN ........................................................................ 234 6.4.1.1 Historical Background ....................................................... 234 6.4.1.2 Previous Archaeoastronomical Research .......................... 235 6.4.1.3 Discussion of Digital Archaeoastronomical Analysis and Research Findings ...................................................... 237 6.4.2 TULA .......................................................................................... 256 6.4.2.1 Historical Background ....................................................... 256 6.4.2.2 Previous Archaeoastronomical Research .......................... 258 6.4.2.3 Discussion of Digital Archaeoastronomical Analysis and Research Findings ...................................................... 258 viii  6.5 Archaeoastronomical Analyses of Selected Aztec Sites ................................ 271 6.5.1 TENOCHTITLAN ...................................................................... 271 6.5.1.1 Historical Background ....................................................... 271 6.5.1.2 Previous Archaeoastronomical Research .......................... 273 6.5.1.3 Discussion of Digital Archaeoastronomical Analysis and Research Findings ...................................................... 275 6.5.2 TLALTELOLCO ........................................................................ 296 6.5.2.1 Historical Background ....................................................... 296 6.5.2.2 Previous Archaeoastronomical Research .......................... 296 6.5.2.3 Discussion of Digital Archaeoastronomical Analysis and Research Findings ...................................................... 297 6.5.3 TENAYUCA............................................................................... 310 6.5.3.1 Historical Background ....................................................... 310 6.5.3.2 Previous Archaeoastronomical Research .......................... 310 6.5.3.3 Discussion of Digital Archaeoastronomical Analysis and Research Findings ...................................................... 311 6.5.4 SANTA CECILIA ACATITLAN............................................... 326 6.5.4.1 Historical Background ....................................................... 326 6.5.4.2 Previous Archaeoastronomical Research .......................... 326 6.5.4.3 Discussion of Digital Archaeoastronomical Analysis and Research Findings ...................................................... 326 6.5.5 TEOPANZOLCO ....................................................................... 339 6.5.5.1 Historical Background ....................................................... 339 6.5.5.2 Previous Archaeoastronomical Research .......................... 340 6.5.5.3 Discussion of Digital Archaeoastronomical Analysis and Research Findings ...................................................... 340 6.6 Chapter Summary........................................................................................... 353 Chapter 7: Conclusion ...............................................................................................................356 Bibliography ...............................................................................................................................365  ix  List of Tables  Table 2.1. Summary of the type of architectural and urban depictions in Pictorial Manuscripts. ............................................................................................................... 47 Table 2.2. Frequency of the type of architectural depictions in Pictorial Manuscripts. ............... 48 Table 4.1. Archeological remains of shrines located on high mountain shrines (Montero 2004) ........................................................................................................................ 141 Table 6.1. Rising and setting times for the Sun in Tenochtitlan, LAT 19.434921, LON -99.131362 on the astronomical horizon from January to June (2012). Cells in columns indicate the time when the first and last appearances of the upper limb of the solar disk occur during  sunrise and sunset respectively. (Table by the Astronomical Applications Department of the U.S. Naval Observatory Data Services). ................................................................................................................. 196 Table 6.2. Altitude and azimuth for the Sun in Tenochtitlan, LAT 19.434921, LON -99.131362 on the astronomical horizon on June 21st, 2012. Sunrise occurs between 6:00 and 6:10 when the Sun rises from the horizon at an azimuth between 64.8 and 65.6. (Table by the Astronomical Applications Department of the U.S. Naval Observatory Data Services). ....................................................... 197 Table 6.3. Prominent peaks on the horizon viewed from Tenochtitlan ...................................... 205 Table 6.4. Main topographic and solar references of Tenochtitlan on the eastern horizon (96.5° axis). .............................................................................................................. 226  x  List of Figures  Figure 1.1. El Cerrito (translated as "The Little Mountain") archaeological site in the state of Querétaro, Mexico. Except for some walls of the platforms and fragments of stairs, most of it remained uncovered until 1995, when excavations officially began.  Only the main façade has been partially restored (Photograph by Julià Sastre - CC-BY 2.0). .................................................................................................... 2 Figure 2.1. Classification of Primary Sources. ............................................................................. 18 Figure 2.2. Engraving of the Templo Mayor by Théodore De Bry, published in 1601 to illustrate the history of José de Acosta (Boone 1987: Figure 6). ............................... 20 Figure 2.3. Engraving of the Templo Mayor, published in 1684 to illustrate the history of Antonio de Solís (Boone 1987: Figure 7). ................................................................. 21 Figure 2.4. Front page and monuments number 8 and 19 in the Descripción de Antiguos Monumentos Mexicanos by Guillermo Dupaix (López Luján 2001:  Figures on pages 72, 74 and 79). ................................................................................................. 22 Figure 2.5. Plan of the ceremonial precinct and the Templo Mayor by Leopoldo Batres published in 1902 (Boone 1987:Figure 26). .............................................................. 24 Figure 2.6. Discovery of the Coyolxauhqui in 1978 (Photograph by Rescate Arqueológico-INAH). ........................................................................................................................ 26 Figure 2.7. (a) Calendar, folios 2v and 3r; (b) Departure from Aztlan, each group is represented as a house glyph, folio 4r, Codex Aubin (British Museum, CC-BY-NC-SA 4.0). ............................................................................................................... 29 Figure 2.8. Departure from Aztlan, Codex Azcatitlan, folio 2 (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0). .................................................................................... 31 Figure 2.9. (a) Tonalpohualli (divinatory calendar) panel with deities looking at stars (represented by half circle with small white dots) and Sun (represented with the other half as a solar disk), folio 11; (b) Deities within a temple in the New Fire ceremony, folio, 34, Codex Borbonicus (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0). .................................................................................... 32 Figure 2.10. (a) Tonalpohualli panel with deities playing on the Tlachtli (ball court), folio 21; (b) 20-day signs distributed over the bodies of four deities, surrounded by xi  four great serpents, associated with the four directions, folio 72, Codex Borgia (Biblioteca Apostolica Vaticana, CC-BY-NC-SA 4.0). ............................................ 34 Figure 2.11. Departure from Aztlan, Codex Boturini (Museo Nacional de Antropología, CC-BY-NC-SA 4.0). ................................................................................................. 35 Figure 2.12. (a) Priest and sacrificed victim with temple in the background, folio 99v; (b) a representation of the god Tlaloc on top of platforms, possibly temalacatl, folio 110v; (c) Templo Mayor in Tetzcoco, folio 112v, Codex Ixtlilxochitl (Bibliothèque Nationale de France ,CC-BY-NC-SA 4.0). ........................................ 36 Figure 2.13. (a) Priest and sacrificed victim with temple in the background, folio 40r (b) a representation of the god Tlaloc on top of platforms, possibly temalacatl, folio 70r, Codex Magliabechiano, Nuttal facsimile (Biblioteca Nazionale Centrale di Firenze, CC-BY-NC-SA 4.0). ............................................................................... 37 Figure 2.14. (a) Events related to famine suffered between 1504 and 1506 described in the context of a temple and sacrificial victim on frame assembled on platform, folio 41v; (b) battle between Mexico and Tlatelolco with double teocalli in the background, folio 26v, Codex Telleriano-Remensis, Loubat facsimile (Biblioteca Nazionale Centrale di Firenze, CC-BY-NC-SA 4.0). ............................ 39 Figure 2.15. Map 9, Codex Xolotl (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0). ............................................................................................................................ 41 Figure 2.16. (a) Migration scene in which two different temples are depicted, one in the traditional way (small mountain with stairs in the lower middle section), and the other with Spanish imagery (lower right), folio 7v; (b) players with ball in the characteristic I-shaped Tlachtli, folio 16v, Historia Tolteca Chichimeca (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0). ........................................ 43 Figure 2.17. Mapa de Cuauhtinchan No. 2 (Carrasco and Sessions 2007:Figure 1). ................... 44 Figure 2.18. Depiction of Palace (Tetzcoco), Mapa Quinatzin (Enhanced copy, original Bibliothèque Nationale de France CC-BY-NC-SA 4.0), .......................................... 45 Figure 2.19. (a) Foundation of Tenochtitlan, folio 2r; (b) tribute list with number of items in Aztec units, folio 24r, Codex Mendoza (Bodleian Library, CC-BY-NC-SA 4.0). ............................................................................................................................ 52 xii  Figure 2.20. (a) and (b) Perimeter dimensions of property in Aztec units and tribute owned, Codex of the Marquesado Del Valle (Archivo General de la Nación de México, CC-BY-NC-SA 4.0). ................................................................................................. 53 Figure 2.21. Plan and Title of a Property in Tenochtitlan (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0). .................................................................................... 54 Figure 2.22. (a) Demographic composition of each household; (b) drawings of parcels with area and perimeter measurements in Aztec units (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0). .................................................................................... 55 Figure 2.23. Plan of palace and surrounding land in Aztec units (upper left corner) and land parcels shape and dimensions in Aztec units (right half of image), Oztoticpac Lands Map (Library of Congress Geography and Map Division Washington, D.C., CC-BY-NC-SA 4.0). ........................................................................................ 57 Figure 2.24. Map of Tenochtitlan from the Latin translation published in Nuremberg in 1524. The map is rotated 90° clockwise while the ceremonial precinct is rotated 90° counterclockwise (Newberry Library, Chicago, CC-BY-NC-SA 4.0). ............................................................................................................................ 60 Figure 2.25. Historia Verdadera de la Conquista de la Nueva España (University of British Columbia-Rare Books and Special Collections). ...................................................... 62 Figure 2.26. Quauitleoa (top); Tlacaxipehualiztli festival within an architectural arrangement that includes two temples, a central platform, and a tzompantli or skull rack (middle); and Tozoztontli festival (bottom), folio 250r, Primeros Memoriales (Real Biblioteca de Madrid, CC-BY-NC-SA 4.0). ............................... 65 Figure 2.27. Depiction of the ceremonial precinct, Primeros Memoriales, folio 268ra (Real Biblioteca de Madrid, CC-BY-NC-SA 4.0). ............................................................. 66 Figure 2.28. (a) Double Teocalli dedicated to Tlaloc and Huitzilopochtli, Cerro Tlaloc and Cerro Telapon frame the twin temples, folio 131r; (b) victim on Temalacatl platform fighting warrior, Historia de las Indias de Nueva España e islas de la Tierra Firme by Diego Durán (Biblioteca Nacional de España, CC-BY-NC-SA 4.0). ...................................................................................................................... 68 Figure 2.29. Map of Valley of Mexico in 1519 (Pasztory 1983: Figure 1). ................................. 71 xiii  Figure 2.30. (a) The Aztec Sun Stone, (b) the ex-Archbishopric's Stone, (c) the Teocalli (Museo Nacional de Antropología, Mexico CC BY-NC-SA 4.0). ............................ 73 Figure 2.31. "Mexican Antiquities," the back of the Teocalli de la Guerra Sagrada and a small single teocalli can be seen in the lower left corner (Lithograph by Decaen 1856). ......................................................................................................................... 74 Figure 2.32. (a) Model in the American Museum of Natural History, New York; (b) model in the Museo de las Américas, Madrid; (c) model in the Musée du quai Branly, Paris (CC BY-NC-SA 4.0). ....................................................................................... 75 Figure 2.33. Three teocalli models with different representations on the top platform. The first model has a temple, the second a solar deity and the third a single deity (British Museum, CC BY-NC-SA 4.0)...................................................................... 76 Figure 2.34. (a) Google Earth view of Plazuelas, (b) model of Plazuelas carved in stone (Photograph by Juan Antonio Siller - CC:BY), (c) aerial view of Plazuelas (Map data: Google Earth). ......................................................................................... 77 Figure 2.35. Drawing of the model at Acalpixan (Broda 2000:Figure 17)................................... 78 Figure 2.36. A collection of pecked cross petroglyphs from Teotihuacan (Aveni 2001:Figure 126). ...................................................................................................... 78 Figure 3.1. From left to right, examples of the Single Temple Teocalli architectural type: depiction within a codex, small scale model, archaeological remains and plan view. ........................................................................................................................... 86 Figure 3.2. From left to right, examples of the Double Teocalli architectural type: depiction within a codex, small scale model, archaeological remains and plan view. .............. 88 Figure 3.3. From left to right, examples of the Circular Base Teocalli architectural type: depiction within a codex, small scale model, archaeological remains and plan view. ........................................................................................................................... 90 Figure 3.4. From top to bottom, examples of the Warriors Precinct within the Teocalli architectural type: depiction within a codex, small scale model, archaeological remains and plan view. .............................................................................................. 92 Figure 3.5. From left to right, examples of the Tzompantli architectural type: depiction within a codex, small scale model, archaeological remains and plan view. .............. 94 xiv  Figure 3.6. From left to right, examples of the Tlachtli architectural type: depiction within a codex, small scale model, archaeological remains and plan view. ......................... 96 Figure 3.7. From left to right, examples of the Momoztli architectural type: depiction within a codex, digital reconstruction, archaeological remains and plan view. ........ 98 Figure 3.8. From left to right, examples of the Central Momoztli architectural type: depictions within codices, archaeological remains and plan view. ......................... 100 Figure 3.9. From left to right, examples of the Temalacatl architectural type: depictions within a codex, monumental sculpture and archaeological remains. ...................... 102 Figure 3.10. From top to bottom, examples of the Calmecac architectural type: depictions within codices and archaeological remains. ............................................................ 104 Figure 3.11. From left to right, examples of Coatepantli and Perimeter wall of ceremonial precinct architectural type: depictions within a codex and archaeological remains. .................................................................................................................... 106 Figure 3.12. Examples of Nobility Dwellings architectural type within codices. ...................... 108 Figure 3.13. Examples of Commoner Dwellings architectural type within a codices and administrative-legal documents. .............................................................................. 110 Figure 3.14. Examples of the Temazcalli architectural type within codices. ............................. 112 Figure 3.15. Clockwise, examples of the Gardens and Pools architectural type: depiction within a codex, archaeological remains and plan. ................................................... 114 Figure 3.16. From top to bottom, examples of the Market architectural type: depictions within a codex and a contemporary market. ............................................................ 116 Figure 3.17. From top to bottom, examples of Chinampas: depictions within a codex and administrative-legal documents and contemporary chinampas. .............................. 119 Figure 3.18. From left to right, examples of Aqueducts and Dykes: depiction of aqueduct within codex and contemporary aqueduct; depiction of dyke within map and contemporary dyke. ................................................................................................. 120 Figure 3.19. Examples of the central ceremonial plaza plan characterized by a major teocalli serving as a focal point in an orthogonal layout within a plaza. ................. 122 Figure 4.1. The aged primordial couple, Oxomoco engaged in divining with maize kernels and her partner, Cipactonal, holding an incense container and burner, Codex Borbonicus folio 19 (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0). ..... 126 xv  Figure 4.2. (a) Huitzilopochtli armed for war with a fire serpent called Xiuhcoatl, Codex Tovar, 1a (Jean Carter Library at Brown University, CC-BY-NC-SA 4.0); (b) Coyolxauhqui Stone found at the Huey Teocalli (Museo del Templo Mayor-INAH). ...................................................................................................................... 127 Figure 4.3. The deity Ometeotl and the layers of the heavens (left); two lowest layers of heavens, above the layer of the Earth and the underworld, Codex Vaticanus A/Loubat, folios 1v and 2r (FAMSI CC-BY-NC-SA 4.0). ..................................... 128 Figure 4.4. The cosmogram in the Codex Fejérváry-Mayer, folio 1, depicting time and space (Museum of the City of Liverpool CC-BY-NC-SA 4.0). .............................. 129 Figure 4.5. The Aztec concept of space and time (Aguilar 2007:Figure 11.5). .......................... 130 Figure 4.6. The four quadrants in the universe bounded by solstice points (González 1975:140). ................................................................................................................ 131 Figure 4.7. Axial orientations of Central Mexican Ceremonial Centres (Aveni and Gibbs 1976: Figure 1). ....................................................................................................... 132 Figure 4.8. The Aztec Tonalpohualli calendar and the four directions of the world with the Sun in the centre, Codex Tovar, folio 142 (John Carter Library at Brown University CC-BY-NC-SA 4.0)............................................................................... 132 Figure 4.9. Representation of the Tonalpohualli cycle in which 20 day names interlock with 13 day numbers (Aguilar 2007:Figure 11.1). .................................................. 133 Figure 4.10. Calendar wheel illustrating the division of the 52-year cycle, Códices Matritenses, folio 188 (Real Biblioteca de Madrid, CC-BY-NC-SA 4.0) . ............. 134 Figure 4.11. The Boban Calendar Wheel where Aztec architectural building types such as a double temple teocalli and nobility palaces are utilized to describe three main events in the history of Texcoco. These buildings are surrounded by a calendar wheel containing the 20-day glyphs (John Carter Library at Brown University CC-BY-NC-SA 4.0).  .............................................................................................. 135 Figure 4.12. Horizon calendar of east as viewed from the Templo Mayor (Aveni, Calnek, Hartung 1988:Figure 5). .......................................................................................... 137 Figure 4.13. Depiction of Tlaloc in the Codex Borbonicus, folio 5 (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0).  ............................................................................ 138 xvi  Figure 4.14. (a) The caves of Chicomoztoc from which the Aztecs emerged, Historia Tolteca-Chichimeca, folio 16r (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0); (b) Tlaloc seated on his mountain temple, Codex Borbonicus, folio 25 (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0). ........................ 139 Figure 4.15. Tetzacualco mountain shrine on the summit of Cerro Tlaloc, (a) plan (Iwaniszewski 1994:Figure 3); (b) view towards the east where other mountains and volcanoes can be observed at a distance (Universidad Autónoma del Estado de Mexico 2010:Page 5). ..................................................... 140 Figure 4.16. Register of the archaeological sites found on Volcán Iztaccihuatl (Montero: Figure 2004:75). ...................................................................................................... 141 Figure 5.1. The Sun god in front of the solar disk, the sky (black band with small circles), the Moon (water-filled vessel with a rabbit), and the Earth (Earth monster below animal sacrificing a quail to the Sun) depicted within a trecena (13-day period) of the Tonalpohualli (260-day ritual calendar), Codex Borgia, folio 51 (Biblioteca Apostolica Vaticana, CC-BY-NC-SA 4.0).  ......................................... 145 Figure 5.2. Aztec astronomers observing the sky (represented a black semi-sphere with small white and red eyes), Codex Mendoza, folio 63 (Bodleian Library, CC-BY-NC-SA 4.0). ...................................................................................................... 147 Figure 5.3. The Atamalqualiztli Festival which was celebrated every eight years; during this time they only ate tamales made with water and salt, Primeros Memoriales, folio 254r (Real Biblioteca de Madrid, CC-BY-NC-SA 4.0). ............ 148 Figure 5.4. Eclipses of Moon and Sun, Primeros Memoriales, folio 282r (Biblioteca Medicea Laurenziana, Firenze, CC-BY-NC-SA 4.0). .............................................. 149 Figure 5.5. Aztec constellations, left (from top to bottom) Mamalhuaztli, Tianquiztli, Citlaltlachtli; right (from top to bottom Citlalxonecuilli, Citlalcolotl, Primeros Memoriales, folios 282 r y 282v (Biblioteca Medicea Laurenziana, Firenze, CC-BY-NC-SA 4.0). ............................................................................................... 150 Figure 5.6. (a) Astronomer using a pair of crossed-sticks set up on top of a temple to determine a position of a celestial body; (b) An arrangement of two crossed-sticks through which an astronomer views a V-shaped arrangement in the xvii  distance, where a celestial body, probably the Sun, can be seen, Codex Bodley, plate 15 (Bodleian Library, CC-BY-NC-SA 4.0). ................................................... 151 Figure 5.7. Ceremonial precinct depicted on the Map of Tenochtitlan included in the Second Letter of Cortes published printed in celebriciuitate Norimberga [Nuremberg] in 1524. Even though the ceremonial centre was rotated -90° from its real orientation, the face of the Sun is depicted as an animate being seen emerging between the twin temples of the Huey Teocalli (Newberry Library, Chicago, CC-BY-NC-SA 4.0). .................................................................. 152 Figure 5.8. Orienting of a temple towards the Sun on the horizon and adjusting an orientation of Sun at horizon to Sun over temple (Aveni, Calnek and Hartung 1988:Figure1). ......................................................................................................... 153 Figure 5.9. (a) The annual path of Earth around the Sun. (b) The tilt of the Earth's axis in the plane of the ecliptic results in the seasonal variations (Stein, et al. 2006:150). ................................................................................................................ 154 Figure 5.10. (a) The position of the Sun is expressed in terms of the vertical angle above the horizon (altitude) and the horizontal angle (azimuth). (b) Approximate position of the Sun in each of the seasons at a mid-northern latitude. Note that the altitude angle is maximum in the summer, minimum in the winter, and in between in spring and fall (Stein, et al. 2006:151). ................................................. 155 Figure 5.11. (a) The sky vault is represented as a hemisphere, which projects as a circle (b) on a projection plane. The exact shape of the Sun path chart depends upon the projection method. The hour points of the Sun path chart are connected to form hour lines that are useful for interpolation (Stein, et al. 2006:154). ........................ 156 Figure 5.12. Equidistant (horizontal, polar) Sun path diagram for 44 degrees latitude (Stein, et al. 2006:156). ............................................................................................ 157 Figure 5.13. Aztec numerals(a) 1; (b) 20; (c) 400; (d) 8000 (Closs 2008:Figure1). .................. 158 Figure 5.14. Contexts of Aztec numeral usage. Calendar dates: (a) 13 Rabbit; (b) 8 Reed. Chronological counts: (c) 70 years; (d) 5206 years. Tribute records: (e) 100 copper hatchets; (f) 1200 coarse clay pots; (g)   8000 balls of unrefined copal wrapped in palm leaves (Closs 2008:Figure2). ....................................................... 158 xviii  Figure 5.15. Tributes of Tlaxinican, Tlaylotlacan, Tecpanpa, etc. depicting number—represented by symbols on above objects—coins, fish, and waterfowl paid as tribute to Colonial authorities (Archivo General de la Nación de México ,CC-BY-NC-SA 4.0). ...................................................................................................... 159 Figure 5.16. Plan and title of a property in Huexocolco, depicting measurements—represented by dots around the perimeter—of house and chinampas (Archivo General de la Nación de México ,CC-BY-NC-SA 4.0). ......................................... 160 Figure 5.17. A land record from the codex Santa María Asunción (Harvey and Williams 1980:Figure 1). ........................................................................................................ 161 Figure 5.18. Acolhua equivalences inferred from computation of Acolhua recorded areas. The hand, heart and arrow are referents for proportions 5:3, 5:2 and 2; the bone and arm are tentatively proposed glyphic referents for proportions 5:1 and 3:1 (Williams and Jorge 2008:Figure 2). ....................................................................... 162 Figure 5.19. Measurements of property in hands, hearts and arrows, House of Ana Justina, San Hipólito Teocatilan District, 1593 (Archivo General de la Nación de México ,CC-BY-NC-SA 4.0). .................................................................................. 162 Figure 5.20. Aztec units of measure and their body referents (Clark 2010:Figure 12.1). .......... 163 Figure 5.21. Aztec linear measures and their metric values (Clark 2010:Table12.1). ............... 164 Figure 5.22. Property titles of Tenochtitlan utilizing two types of numeral, one for quantities (blue flag and dots on top) and measurements of house in hands, dots and arrows (Archivo General de la Nación de México, CC-BY-NC-SA 4.0). .......................................................................................................................... 165 Figure 5.23. Diagram of the Mesoamerican Orientation System. The alignments are in accordance with the hypothetical solar orientation calendar with 13-day weeks. The clockwise deviations from east represent the "winter sunrise Maya type" and the deviations from West, the "Summer Sunset Central Mexico Type" (Tichy 1988:Figure7). .............................................................................................. 166 Figure 5.24. Reconstruction of an astronomical device based on an illustration in the Codex Selden that was probably used throughout Mesoamerica. It is the size of a hand with spread fingers and made of a bundle of twigs. When the hand is xix  outstretched, the angle between the two tips, which are 4.3 cm apart, is 4.5 degrees or 1/20th of a right angle (Tichy 1988:Figure 9). ........................................ 167 Figure 5.25. The geometric composition deduced by Oliverio Sánchez based in two interrelated pentagons (Ramirez 1995:Figure 16). .................................................. 168 Figure 5.26. Geometric study of the Coatlicue (Martínez 2004:Figure 5.44). ........................... 168 Figure 5.27. Plan of Teotihuacan with possible measured distances indicated in TMU (Sugiyama 2010:Figure 11.3). ................................................................................. 169 Figure 5.28. Schematic representation of the Aztec worldview (Matos 1988:Figure 107). ....... 171 Figure 5.29. Underlying polygons in the Aztec Sun stone (Ramírez 1995:Figure 29). ............. 172 Figure 5.30. Superimposed isosceles triangles in the Tizoc Stone (Ramírez 1995: 95). ............ 173 Figure 5.31. Σ rectangle 7 x 8 (Martinez 2000:Figures 2.6 and 2.7). ......................................... 174 Figure 5.32. Plan of the Sun Pyramid complex with the Avenue of the Dead with measurements in meters and TMU (Sugiyama 2010:Figure 11.5). ......................... 175 Figure 5.33. (a) Stone panel on wall of the Monjas complex at Chichen Itza, (b) Geometric analysis of panel (Amábilis 1956:Figure 75)........................................................... 176 Figure 5.34. Digital interpretation of the ceremonial precinct of Tenochtitlan based on the geometric and archaeoastronomical analyses performed in the urban arrangement and each architectural type; (a) regulating lines of the Huey Teocalli; (b) digital interpretation with structures found in both ethno-historical sources and archaeological records (Rivera 1996). ................................................. 177 Figure 5.35. (a) A calpulli, (b) Parents delivering their sons to the Calmecac, (c) Calmecac priest addressing students, Florentine Codex, Books 2, 3, and 2 respectively (Biblioteca Medicea Laurenziana, Firenze, CC-BY-NC-SA 4.0). ......................... 179 Figure 5.36. "De los diferentes edificios" ("About the different buildings"); a double teocalli depicted on the left, and a tradesman building the teocalli on the right, Florentine Codex, folios 240r and 241v (Biblioteca Medicea Laurenziana, Firenze, CC-BY-NC-SA 4.0). ................................................................................. 180 Figure 5.37. The carpenter, Florentine Codex, Book 10, folio 17r (Biblioteca Medicea Laurenziana, Firenze, CC-BY-NC-SA 4.0). ........................................................... 181 xx  Figure 5.38. (a) Several activities performed by stonemasons, Florentine Codex, folio 20v; (b) Mason and assistant preparing sand for plaster, folio 20r (Biblioteca Medicea Laurenziana, Firenze, CC-BY-NC-SA 4.0). ............................................ 182 Figure 5.39. Female painter, Codex Telleriano-Remensis, lower left corner of folio v (Biblioteca Medicea Laurenziana, Firenze, CC-BY-NC-SA 4.0). ......................... 183 Figure 5.40. (a) Strategizing for a battle with a plan of the building they intend to attack, folio 33r (Biblioteca Medicea Laurenziana, Firenze, CC-BY-NC-SA 4.0); (b) Preparing colours for scribe seen writing on paper, (Biblioteca Medicea Laurenziana, Firenze, CC-BY-NC-SA 4.0);(c) The people of Xochimilco building a causeway, depicted by several tradesmen, tools (including a measuring cord) and a group of three men receiving instructions from the emperor, Durán, plate 13, chapter 8 (Biblioteca Nacional de España, CC-BY-NC-SA 4.0). ............................................................................................................. 185 Figure 5.41. Enlargement of a temple in Tlatelolco utilizing several trades and construction materials, Codex Azcatitlan, folio 14 (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0). ...................................................................................................... 187 Figure 5.42. (a) Carpenter tools, folio 17r; (b)Stonemason tools, folio 20r, (Biblioteca Medicea Laurenziana, Firenze, CC-BY-NC-SA 4.0). ............................................ 188 Figure 5.43. Arte de la lengua mexicana y castellana published by Alonso de Molina in 1571 (Newberry Library, CC-BY-NC-SA 4.0). ...................................................... 189 Figure 5.44. (a) Folio 10 displaying gods, mountains, buildings and figures with measuring cord on lower right; (b) detail of folio 10; (c) Folio 5 displaying gods, mountains, buildings and figures with measuring cord on middle right section; (d) detail of folio 5; all Facsimiles of the Codex Vindobonensis Mexicanus 1, Kingsborough Volume II (FAMSI CC-BY-NC-SA 4.0). ....................................... 190 Figure 6.1. Sun path polar chart of Tenochtitlan, LAT 19.434921, LON -99.131362 on the astronomical horizon indicating the apparent seasonal-and-hourly positional changes of the Sun as the Earth rotates and orbits around the Sun. Azimuth angles run around the edge of the diagram; altitude angles are represented as concentric circular lines that run from the center of the diagram out; date lines start on the eastern side of the graph and run to the western side and represent xxi  the path of the Sun  on one particular day of the year; hour lines are shown as dotted blue lines that intersect the date lines and represent the position of the Sun at a specific hour of the day. The intersection points between date and hour lines give the position of the Sun (Polar chart by the University of Oregon, Solar Radiation Monitoring Laboratory). .................................................. 195 Figure 6.2. View of the binary volcanic system composed by the Volcán Iztaccihuatl and the Volcán Popocatepetl—with a fumarole coming out from its cone—seen from the tetzacualco located on the summit of Cerro Tlaloc. The closer mountain to the right is Cerro Telapon (Photograph by José Luis – CC:BY). ........ 198 Figure 6.3. Interpretation of the Sun rising in the notch of the Great Temple on March 21st by Aveni which presupposes the height of the Templo Mayor and the existence — at a certain distance and height — of a circular temple where this event was viewed (Aveni and Gibbs 1978: Figure 4). ............................................................. 199 Figure 6.4. Archaeological remains of the Great Teocalli of Tenochtitlan, scale 1:200. The streets of present day Mexico City follow the same azimuthal direction of 96.5° ± 0.5° of the Great Teocalli (Map data: Google Earth).................................. 204 Figure 6.5. Prominent peaks around Tenochtitlan, scale 1:10,000 Yellow triangles, which indicate larger peaks, are identified as "volcán" (volcano), while green triangles, which indicate smaller peaks, are identified as "cerro" (mountain), regardless of their geological origins (Map data: Google Earth). ........................... 206 Figure 6.6. Viewshed of Tenochtitlan shown as red shaded areas and prominent peaks on the horizon, scale 1:10,000 (Map data: Google Earth and TA). .............................. 208 Figure 6.7 Alignment reference diagram superimposed on topographic landscape of Tenochtitlan. Tentative alignments to prominent peaks on the horizon can be observed on solstitial/equinoctial and urban axes, scale 1:10,000. (Map data: Google Earth, AutoCAD, TA and CGA). ................................................................ 210 Figure 6.8. Position of the rising Sun between Cerro Tlaloc (also known as Mount Tlaloc) and Cerro Telapon along the 96.5° urban east-west axis of Tenochtitlan considering topographic altitude and the curvature of the Earth. The thick yellow line indicates the sunrise azimuth in the astronomical horizon. The fine yellow line indicates the sunrise azimuth in the local horizon, which xxii  corresponds to the real position of the Sun viewed from the site (Map data: Google Maps, INEGI and SCA). ............................................................................. 212 Figure 6.9. Position of the setting Sun on nondescript topographic feature along the 96.5° urban east-west axis of Tenochtitlan considering topographic altitude and the curvature of the Earth. The thick red line indicates the sunset azimuth in the astronomical horizon. The fine red line indicates the sunset azimuth in the local horizon, which corresponds to the real position of the Sun viewed from the site (Map data: Google Maps, INEGI and SCA). .......................................................... 214 Figure 6.10. Alignment of Tenochtitlan to the highest peak of Pico Tres Padres (within the Sierra of Guadalupe) along its the urban north axis (marked on diagram as NE axis). This diagram contains three views from Tenochtitlan to the highest point of Pico Tres Padres: a 360° topographic panorama showing the alignment, a topographic profile section and an aerial view (Map data: Google Maps and TA). .......................................................................................................................... 216 Figure 6.11. Alignment of Tenochtitlan to the intermediate point (19.391519°, -98.716064°) between the binary volcanic system of Cerro Tlaloc and Cerro Telapon along its the urban east axis (marked on diagram as SE axis). This diagram contains three views from Tenochtitlan to Cerro Tlaloc and Cerro Telapon: a 360° topographic panorama showing the alignment, a topographic profile section and an aerial view (Map data: Google Maps and TA). .................... 218 Figure 6.12. Alignment of Tenochtitlan to Cerro Acopiaxco (within the Chichinautzin volcanic field and lava caves) along its the urban south axis (marked on diagram as SW axis). This diagram contains three views from Tenochtitlan to Cerro Acopiaxco: a 360° topographic panorama showing the alignment, a topographic profile section and an aerial view (Map data: Google Maps and TA). .......................................................................................................................... 220 Figure 6.13. Alignment of Tenochtitlan to a nondescript topographic feature along its the urban west axis (marked on diagram as NW axis). This diagram contains three views from Tenochtitlan to Cerro Tlaloc and Cerro Telapon: a 360° topographic panorama showing the alignment, a topographic profile section and an aerial view (Map data: Google Maps and TA). ............................................ 222 xxiii  Figure 6.14. Position of the rising Sun during the equinox on the true eastern horizon. This diagram contains three views from Tenochtitlan to the base of Cerro Tlaloc: a 360° topographic panorama showing the alignment, a topographic profile section and an aerial view. The solstitial/equinoctial points are marked as black dots and the site alignment (urban east) is marked as a red dot in the panorama (Map data: Google Maps and TA). .......................................................................... 224 Figure 6.15. Main solar references on the 96.5° eastern horizon calendar of Tenochtitlan where the Sun rises between Cerro Tlaloc and Cerro Telapon on March 6 and October 7. The coloured bar on the right indicates the distance to the topographic features; the red and green line indicate azimuthal directions; and the dotted lines indicate the positions of the Sun on the solstices, equinoxes and the alignment date. The white line shows how this horizon calendar was utilized to count the days between these events so as to calculate the months in the Aztec calendar. The circular image on the urban east axis is a detail of the Great Teocalli taken from the Nuremberg Map where the Sun (depicted as a face) can be seen rising between the twin temples of Tlaloc and Huitzilopochtli. This event was recreated on a sacred landscape when the Sun came out between Cerro Tlaloc and Cerro Telapon (Map data: Google and INEGI). .................................................................................................................... 229 Figure 6.16. Main solar references on the 97.0° eastern horizon calendar of Tenochtitlan where the Sun rises between Cerro Tlaloc and Cerro Telapon on March 4 and October 9 in 73-days intervals related to Venus (Map data: Google and INEGI). .................................................................................................................... 230 Figure 6.17. Main eastern alignments of Tenochtitlan. True cardinal directions are indicated as black dotted lines; the main urban axes of Tenochtitlan are indicated as black lines. The interactions between the urban north-south-east-west axes with the topography reveal the urban design principles of Tenochtitlan. Furthermore, the direction of the urban east axis reveals the architectural design principles of the Great Teocalli, the unique Aztec architectural form characterized by double temples. ............................................... 232 xxiv  Figure 6.18. Location of Teotihuacan indicating prominent peaks around the site, scale 1:10,000. Yellow triangles, indicating larger peaks, are identified as "volcán" (volcano), while green triangles, indicating smaller peaks, are identified as "cerro" (mountain), regardless of their geological origins (Map data: Google Earth). ...................................................................................................................... 243 Figure 6.19. Aerial view of the archaeological remains of Teotihuacan, scale 1:200 (Map data: Google Earth). ................................................................................................. 244 Figure 6.20. Plan of archaeological remains of Teotihuacan (Teotihuacan Mapping Project from Millon 1973:Map 1). ....................................................................................... 245 Figure 6.21. Alignment reference diagram superimposed on topographic landscape of Teotihuacan. Tentative alignments to prominent peaks on the horizon can be observed on solstitial/equinoctial and urban axes, scale 1:10,000. (Map data: Google Earth, AutoCAD, TA and CGA). ................................................................ 246 Figure 6.22. Alignment of Teotihuacan to Cerro Gordo along its the urban north axis, marked on diagram as NE axis (Map data: Google Maps and TA). ........................ 247 Figure 6.23. Alignment of Teotihuacan to a point 561 metres south of Cerro Colorado along its the urban east axis, marked on diagram as SE axis (Map data: Google Maps and TA). ......................................................................................................... 248 Figure 6.24. Position of the rising Sun along the 105.5° urban east-west axis of Teotihuacan considering topographic altitude and the curvature of the Earth. The thick yellow line indicates the sunrise azimuth in the astronomical horizon. The fine yellow line indicates the sunrise azimuth in the local horizon, which corresponds to the real position of the Sun viewed from the site (Map data: Google Maps, INEGI and SCA). .................................................................... 249 Figure 6.25. Main eastern alignments of Teotihuacan. True cardinal directions are indicated as black dotted lines; the main urban axes of Teotihuacan are indicated as black lines. The interactions between the urban north-south-east-west axes with the topography reveal the urban design principles of Teotihuacan. ............................................................................................................. 250 Figure 6.26. Main solar references on the 105.5° eastern horizon calendar of Teotihuacan and calendar cycle (Map data: Google, INEGI and UDI). ...................................... 251 xxv  Figure 6.27 Viewpoints (clockwise) along the Avenue of the Dead towards the urban north axis where the Pyramid of the Sun and the Pyramid of the Moon emerge from Cerro Gordo. At the end of the spatial sequence, the Pyramid of the Moon becomes the Cerro Gordo (Map data: Google Street View). ................................... 252 Figure 6.28. Viewpoint from the Pyramid of the Moon towards the urban south axis where the Pyramid of the Sun is an integral part of Sierra Patlachique in the southern horizon. Volcán Tlaloc marks the end of the spatial sequence that goes through the Cuevas de Xometla (Map data: Google Street View). ....................................... 253 Figure 6.29. Mapa de San Francisco Mazapan, Teotihuacan (Mapa Saville) re-drawn around 1700 CE where the main urban axes are clearly depicted. The urban axes are marked by the Pyramid of the Moon on the left (north), the perpendicular axis of the Pyramid of the Sun (east) and the Cuevas de Xometla at the end of the axis (south) (American Museum of Natural History, New York,  CC:BY-NC-SA 4.0). .................................................................................... 254 Figure 6.30. Proposed interpretation of the "Tlalocan" mural in Teotihuacan, where the large mountain (Pyramid of the Sun) is connected to a cave (Cuevas de Xometla) through a river (Avenue of the Dead) flanked by land parcels and maize plants; even the configuration of the stairs on the Pyramid of the Sun and the Tlalocan mountain are the same, as they are wide at street level and become more narrow as they reach the top. The graphic representation of the Cuevas de Xometla on the mural is also very similar to its representation on the Mapa Saville. The Pyramid of the Moon was likely depicted on the missing left part of the mural (clockwise, photographs by Jorge Ríos, Ejidos de Xometla and Carlos Sanchez - CC:BY-NC). .......................................................... 255 Figure 6.31. Location of Tula indicating prominent peaks around the site, scale 1:10,000. Yellow triangles, indicating larger peaks, are identified as "volcán" (volcano), while green triangles, indicating smaller peaks, are identified as "cerro" (mountain), regardless of their geological origins (Map data: Google Earth). ........ 262 Figure 6.32. Aerial view of the archaeological remains of Tula, scale 1:200 (Map data: Google Earth). .......................................................................................................... 263 xxvi  Figure 6.33. Plan of archaeological remains of Tula (Mastache and Cobean 2012:Figure 26.4). ........................................................................................................................ 264 Figure 6.34. Alignment reference diagram superimposed on topographic landscape of Tula. Tentative alignments to prominent peaks on the horizon can be observed on solstitial/equinoctial and urban axes, scale 1:10,000. (Map data: Google Earth, AutoCAD, TA and CGA). ....................................................................................... 265 Figure 6.35. Alignment of Tula to Cerro el Magoni along its urban west axis, marked on diagram as NW axis (Map data: Google Maps and TA). ........................................ 266 Figure 6.36. Alignment of Tula to las Lumbreras Springs along its urban east axis, marked on diagram as SE axis (Map data: Google Maps and TA). ..................................... 267 Figure 6.37. Position of the rising Sun along the 103.5° urban east-west axis of Tula considering topographic altitude and the curvature of the Earth. The thick yellow line indicates the sunrise azimuth in the astronomical horizon. The fine yellow line indicates the sunrise azimuth in the local horizon, which corresponds to the real position of the Sun viewed from the site (Map data: Google Maps, INEGI and SCA). ............................................................................. 268 Figure 6.38. Main eastern alignments of Tula. True cardinal directions are indicated as black dotted lines; the main urban axes of Tula are indicated as black lines. The interactions between the urban north-south-east-west axes with the topography reveal the urban design principles of Tula. .......................................... 269 Figure 6.39. Main solar references on the 103.5° eastern horizon calendar of Tula and calendar cycle (Map data: Google, INEGI and UDI). ............................................. 270 Figure 6.40. Accidental discoveries in downtown Mexico City (Matos 1988:Figure 7). .......... 283 Figure 6.41. Plan of archaeological remains of Tenochtitlan (Drawing by Michelle De Anda, Projecto Templo Mayor, Séptima Temporada, INAH, 2013). ...................... 284 Figure 6.42. Venus signs along the edge of the Aztec Sun Stone or Calendar Stone relating the counting of the days of the solar year with the counting of the days of the Venusian year (Photographs by Ian Mursell - CC:BY). .......................................... 285 Figure 6.43. Geometrical exploration of the Aztec migration route following a search pattern where the urban north axis had to align to the highest point of Pico Tres Padres and the urban east axis to the concave space between Cerro Tlaloc and xxvii  Cerro Telapon. Even though there were an infinite set of points along this arc, it was only in the precise location of Tenochtitlan where these axes intersected on March 4 and October 9, a calendrical reference point that alluded to the date of birth of Huitzilopochtli and allowed the division of the year in 73-day intervals related to Venus. ....................................................................................... 286 Figure 6.44. Parroquia de San Miguel Arcángel in contemporary Iztacalco, a small island that was located at the intersection of the true north and true east axes aligning to Pico Tres Padres and the concave space between Cerro Tlaloc and Cerro Telapon. The decoration of the altar with faces inside golden Suns (similar to the Sun with a face depicted between the twin temples of the Huey Teocalli in the Nuremberg Map) as well as the rays emanating from the dome to the altar are probably a reminder of the cultural importance of the Aztec Sun god at this location (Photograph by Enrique López-Tamayo - CC:BY). .................................. 287 Figure 6.45. Birth of Huitzilopochtli on Cerro Coatepec with the date of his birth represented by four nights and three days ending on a star (Venus) to the left of Cerro Coatepec in the Codex Azcatitlan, Folio 6 (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0). .................................................................................. 288 Figure 6.46. Aztec migration route along the Valley of Mexico according to the Codex Azcatitlan (Castañeda 2002:Figure 5). The findings of this research suggest that the westerly locations along this route might have served as viewpoints to calculate the position of the rising sun on the local horizon at a certain date where they could recreate through architecture and urban planning the mythical birth of Huitzilopochtli, the Sun god. ....................................................... 289 Figure 6.47. Interpretation of the Teocalli de la Guerra Sagrada sculpture (Drawings by Marquina 1964:Figures 11 to 14; photograph Museo Nacional de Antropología/INAH CC:BY-NC-SA 4.0). .............................................................. 290 Figure 6.48. Interpretation of the Tlaloc-Tlaltecuhtli sculpture (Photo by Marco Antonio Pacheco/Raíces CC:BY-NC). .................................................................................. 291 Figure 6.49. Interpretation of the Tlaltecuhtli of the Hotel Majestic sculpture(Lopez Luján 2010:91). .................................................................................................................. 292 xxviii  Figure 6.50. Interpretation of the location of the Tlaltecuhtli (three-dimensional scanned model of Tlaltecuhtli) (López Luján 2010:51); reconstructive drawing of the relief sculpture by Julian Romero (López Luján 2010:76); plan of the group of eight caches placed at the cardinal and intercardinal ends of the monolith (Proyecto Templo Mayor/INAH)). ........................................................................... 293 Figure 6.51. From left to right, depictions of the birth of Huitzilopochtli within ethnohistoric sources where Cerro Tlaloc and Cerro Telapon are represented as two straw huts (Codex Aubin Folio 25v) and two mountains at a distance (Durán Folio 14v and Durán Folio 225v). ............................................................... 294 Figure 6.52. Clockwise, several scenes within the Historia de las Indias de la Nueva España by Durán where Cerro Tlaloc and Cerro Telapon are represented as two mountains at a distance. On the scenes to the left, a snake is depicted between two mountains (Biblioteca Digital Hispánica Folios 7v, 18v, 25r 37r, CC:BY-NC-SA 4.0). ................................................................................................ 295 Figure 6.53. Location of Tlatelolco indicating prominent peaks around the site, scale 1:10,000. Yellow triangles, indicating larger peaks, are identified as "volcán" (volcano), while green triangles, indicating smaller peaks, are identified as "cerro" (mountain), regardless of their geological origins (Map data: Google Earth). ...................................................................................................................... 301 Figure 6.54. Aerial view of the archaeological remains of Tlatelolco, scale 1:200 (Map data: Google Earth). ................................................................................................. 302 Figure 6.55. Plan of archaeological remains of Tlatelolco (Guilliem 2008:Figure 2). ............... 303 Figure 6.56. Alignment reference diagram superimposed on topographic landscape of Tlatelolco. Tentative alignments to prominent peaks on the horizon can be observed on solstitial/equinoctial and urban axes, scale 1:10,000. (Map data: Google Earth, AutoCAD, TA and CGA). ................................................................ 304 Figure 6.57. Alignment of Tlatelolco to the highest peak of Pico Tres Padres (within the Sierra of Guadalupe) along its urban north axis (marked on diagram as NE axis). This diagram contains three views from Tenochtitlan to the highest point of Pico Tres Padres: a 360° topographic panorama showing the alignment, a xxix  topographic profile section, and an aerial view (Map data: Google Maps and TA). .......................................................................................................................... 305 Figure 6.58. Alignment of Tlatelolco to the intermediate point (19.391519°, -98.716064°) between the binary volcanic system of Cerro Tlaloc and Cerro Telapon along its urban east axis (marked on diagram as SE axis). This diagram contains three views from Tenochtitlan to Cerro Tlaloc and Cerro Telapon: a 360° topographic panorama showing the alignment, a topographic profile section and an aerial view (Map data: Google Maps and TA). ............................................ 306 Figure 6.59. Position of the rising Sun between Cerro Tlaloc (also known as Mount Tlaloc) and Cerro Telapon along the 98.5° urban east-west axis of Tlatelolco considering topographic altitude and the curvature of the Earth. The thick yellow line indicates the sunrise azimuth in the astronomical horizon. The fine yellow line indicates the sunrise azimuth in the local horizon, which corresponds to the real position of the Sun viewed from the site (Map data: Google Maps, INEGI and SCA). ............................................................................. 307 Figure 6.60. Main eastern alignments of Tlatelolco. True cardinal directions are indicated as black dotted lines; the main urban axes of Tlatelolco are indicated as black lines. The interactions between the urban north-south-east-west axes with the topography reveal the urban design principles of Tlatelolco. .................................. 308 Figure 6.61. Main solar references on the 98.5° eastern horizon calendar of Tlatelolco and calendar cycle (Map data: Google, INEGI and UDI). ............................................. 309 Figure 6.62. Location of Tenayuca indicating prominent peaks around the site, scale 1:10,000. Yellow triangles, indicating larger peaks, are identified as "volcán" (volcano), while green triangles, indicating smaller peaks, are identified as "cerro" (mountain), regardless of their geological origins (Map data: Google Earth). ...................................................................................................................... 316 Figure 6.63. Aerial view of the archaeological remains of Tenayuca, scale 1:200 (Map data: Google Earth). ................................................................................................. 317 Figure 6.64. Plan of archaeological remains of Tenayuca (Acosta 1963:Figure 1). .................. 318 Figure 6.65. Alignment reference diagram superimposed on topographic landscape of Tenayuca. Tentative alignments to prominent peaks on the horizon can be xxx  observed on solstitial/equinoctial and urban axes, scale 1:10,000. (Map data: Google Earth, AutoCAD, TA and CGA). ................................................................ 319 Figure 6.66. Alignment of Tenayuca to the Sierra de Guadalupe along its the urban north axis, marked on diagram as NW axis (Map data: Google Maps and TA). .............. 320 Figure 6.67. Alignment of Tenayuca to the concave space between Cerro del Chiquihuite (4 kilometers) and Cerro Zacatenco (6 kilometers) towards —but not exactly— the concave space between Cerro Tlaloc and Cerro Telapon (48 kilometers) along its the urban east axis, marked on diagram as SE axis (Map data: Google Maps and TA). ......................................................................................................... 321 Figure 6.68. Position of the rising Sun along the 106.5° urban east-west axis of Tenayuca considering topographic altitude and the curvature of the Earth. The thick yellow line indicates the sunrise azimuth in the astronomical horizon. The fine yellow line indicates the sunrise azimuth in the local horizon, which corresponds to the real position of the Sun viewed from the site (Map data: Google Maps, INEGI and SCA). ............................................................................. 322 Figure 6.69. Main eastern alignments of Tenayuca. True cardinal directions are indicated as black dotted lines; the main urban axes of Tenayuca are indicated as black lines. The interactions between the urban north-south-east-west axes with the topography reveal the urban design principles of Tenayuca. .................................. 323 Figure 6.70. Main solar references on the 106.5° eastern horizon calendar of Tenayuca and calendar cycle (Map data: Google, INEGI and UDI). ............................................. 324 Figure 6.71. Drawing of the front view of the construction stages of the main double temple teocalli of Tenayuca where the observation made by Marquina that "the temple on the north always stayed in the same place while the south temple was moved further south at each successive stage" validates the theory proposed in this research that a single teocalli dedicated to Tlaloc was built first to align to Cerro Tlaloc on February 11/12, but that subsequent enlargements had to move and rotate south in order to align to the sacred concave space between Cerro Tlaloc and Cerro Telapon, the mythical space of birth of the Aztec Sun god Huitzilopochtli. This resulted in the offsetting of the architectural axes of the teocalli to the southeast and the site alignment dates xxxi  from February 11/12 to February 8 (Drawing by Marquina 1964:Figure 50 modified by Rivera). ................................................................................................ 325 Figure 6.72. Location of Santa Cecilia Acatitlan indicating prominent peaks around the site, scale 1:10,000. Yellow triangles, indicating larger peaks, are identified as "volcán" (volcano), while green triangles, indicating smaller peaks, are identified as "cerro" (mountain), regardless of their geological origins (Map data: Google Earth). ................................................................................................. 330 Figure 6.73. Aerial view of the archaeological remains of Santa Cecilia Acatitlan, scale 1:200 (Map data: Google Earth). ............................................................................. 331 Figure 6.74. Google street view of archaeological remains of Santa Cecilia Acatitlan (Map data: Google Street View). ...................................................................................... 332 Figure 6.75. Alignment reference diagram superimposed on topographic landscape of Santa Cecilia Acatitlan. Tentative alignments to prominent peaks on the horizon can be observed on solstitial/equinoctial and urban axes, scale 1:10,000. (Map data: Google Earth, AutoCAD, TA and CGA). ............................. 333 Figure 6.76. Alignment of Santa Cecilia Acatitlan to the Sierra de Guadalupe along its the urban north axis, marked on diagram as NW axis (Map data: Google Maps and TA). .......................................................................................................................... 334 Figure 6.77. Alignment of Santa Cecilia Acatitlan to the concave space between Sierra de Guadalupe and Cerro del Chiquihuite towards —but not exactly— the concave space between Cerro Tlaloc and Cerro Telapon along its the urban east axis, marked on diagram as SE Axis. Since the view towards Cerro Tlaloc and Cerro Telapon was partially obstructed by Cerro del Chiquihuite, the founders of Santa Cecilia Acatitlan probably followed the orientation of Tenayuca, located approximately 4 kilometers to the southeast of Santa Cecilia Acatitlan (Map data: Google Maps and TA). ................................................................................... 335 Figure 6.78. Position of the rising Sun along the 106.5° urban east-west axis of Santa Cecilia Acatitlan considering topographic altitude and the curvature of the Earth. The thick yellow line indicates the sunrise azimuth in the astronomical horizon. The fine yellow line indicates the sunrise azimuth in the local horizon, xxxii  which corresponds to the real position of the Sun viewed from the site (Map data: Google Maps, INEGI and SCA). .................................................................... 336 Figure 6.79. Main eastern alignments of Santa Cecilia Acatitlan. True cardinal directions are indicated as black dotted lines; the main urban axes of Santa Cecilia Acatitlan are indicated as black lines. The interactions between the urban north-south-east-west axes with the topography reveal the urban design principles of Santa Cecilia Acatitlan. ...................................................................... 337 Figure 6.80. Main solar references on the 106.5° eastern horizon calendar of Santa Cecilia Acatitlan and calendar cycle (Map data: Google, INEGI and UDI). ....................... 338 Figure 6.81. Location of Teopanzolco indicating prominent peaks around the site, scale 1:10,000. Yellow triangles, indicating larger peaks, are identified as "volcán" (volcano), while green triangles, indicating smaller peaks, are identified as "cerro" (mountain), regardless of their geological origins (Map data: Google Earth). ...................................................................................................................... 344 Figure 6.82. Aerial view of the archaeological remains of Teopanzolco, scale 1:200 (Map data: Google Earth). ................................................................................................. 345 Figure 6.83. Plan of archaeological remains of Teopanzolco (Konieczna 2005:Figure 1). ....... 346 Figure 6.84. Alignment reference diagram superimposed on topographic landscape of Teopanzolco. Tentative alignments to prominent peaks on the horizon can be observed on solstitial/equinoctial and urban axes, scale 1:10,000. (Map data: Google Earth, AutoCAD, TA and CGA). ................................................................ 347 Figure 6.85. Alignment of Teopanzolco to Cerro Tres Cruces along its urban north axis, marked on diagram as NW Axis (Map data: Google Maps and TA). ..................... 348 Figure 6.86. Alignment of Teopanzolco to the concave space between the closest mountains and the Cerros de Hueyapan at the base of Volcán Popocatepetl along its urban east axis, marked on diagram as SE axis. Before it was razed and rebuilt by the Aztecs to align to this direction, the axes of the ceremonial precinct at Teopanzolco probably aligned to the Cerros de Hueyapan during the equinox, a theory proposed in this research (Map data: Google Maps and TA). .......................................................................................................................... 349 xxxiii  Figure 6.87. Position of the rising Sun along the 103.5° urban east-west axis of Teopanzolco considering topographic altitude and the curvature of the Earth. The thick yellow line indicates the sunrise azimuth in the astronomical horizon. The fine yellow line indicates the sunrise azimuth in the local horizon, which corresponds to the real position of the Sun viewed from the site (Map data: Google Maps, INEGI and SCA). .................................................................... 350 Figure 6.88. Main eastern alignments of Teopanzolco. True cardinal directions are indicated as black dotted lines; the main urban axes of Teopanzolco are indicated as black lines. The interactions between the urban north-south-east-west axes with the topography reveal the urban design principles of Teotihuacan. ............................................................................................................. 351 Figure 6.89. Main solar references on the 103.5° eastern horizon calendar of Teopanzolco and calendar cycle (Map data: Google, INEGI and UDI). ...................................... 352  xxxiv  Acknowledgements  I owe a debt of gratitude to the members of my committee, Dr. Michael Blake (Department of Anthropology / Laboratory of Archaeology), Professor Leslie Van Duzer (School of Architecture and Landscape Architecture), Dr. Sherry McKay (School of Architecture and Landscape Architecture) and Sr. Instr. Gregory Johnson (School of Architecture and Landscape Architecture / Department of Civil Engineering) for their support, encouragement and helpful suggestions. The discussions with Dr. Blake were exceptionally enlightening and didactic.  I also thank Dr. Jerzy Wojtowicz (School of Architecture and Landscape Architecture / Warsaw University of Technology), Dr. Marvin Cohodas (Department of Art History, Visual Art & Theory), Dr. Kelly Booth (Department of Computer Science / Imager Graphics Visualization Human Centered Technologies Laboratory), Dr. Ricki Goldman (New York University Steinhardt School of Culture, Education and Human Development / Department of Administration, Leadership, and Technology) and Dr. Anthony Shelton (Department of Art History, Visual Art & Theory / Museum of Anthropology), who provided input at earlier stages of this research. Each contributed much needed expertise and perspective.  This dissertation is built upon the contributions of scholars from several disciplines—archaeology, architecture, art, history, astronomy, geography, geometry, mathematics and religion—who provided the cultural background needed to analyze Aztec architecture and urban planning. I am particularly grateful to Eduardo Matos Moctezuma and Dr. Leonardo López Luján for their lifelong dedication to Aztec scholarship and to their passionate collaborators, the archeologists who work in the Zonas Arqueológicas (Archaeological Zones) and projects of the Instituto Nacional de Antropología (INAH), for their willingness to discuss with me the sites and for their patience, as I spent long periods of time in the sites during my innumerable visits throughout the years.  A special acknowledgement goes to the libraries, archives and institutions around the word that have digitized their collections of cultural content and made them publicly available through portals such as the World Digital Library, the Hathi Trust Digital Library, the Biblioteca Digital xxxv  Hispánica, the Dipòsit Digital de Documents de la Universitat Autònoma de Barcelona, the Gallica-bibliothèque numérique de la Bibliothèque Nationale de France, the Biblioteca Medicea Laurenziana, the digital map of Mexico City at the Uppsala University Library, the Foundation for the Advancement of Mesoamerican Studies, the Biblioteca Digital Mexicana, the Codices del INAH, Amoxcalli and the Mapas, Planos e Ilustraciones from the Archivo General de la Nación, among others. The unprecedented access to historical sources proved to be an invaluable research tool as original documents were meticulously scrutinized for architectural and urban references.  I would also like to thank the Interdisciplinary Studies Graduate Program for their unwavering support and understanding, and to the SAGE (Supporting Aboriginal Graduate Enhancement) Program lead by Dr. Jo-ann Archibald, Q'um Q'um Xiiem, who provided invaluable mentoring during these years.  Finally, and most significantly, I thank my family. Gracias. xxxvi  Dedication  To the memory of my Indigenous relations, for inspiring me. To the memory of my parents Rosa y Abel, for encouraging me. And to my family, Javier, Javier and Joel, for their immeasurable support. Ni mitz tlazojtla ika nochi no yolotl. 1  Chapter 1: Introduction  The historic present of modern Mexico is like a river fed by many streams, both recent and remote in origin, which make up the complex reality of the country today. Each of the historical periods survives in contemporary Mexicans; no matter how distant they may seem, they merge in the present. (López Austin and López Luján 2001:3)  This dissertation rests on a straightforward question: What are the main design principles embedded in Aztec architecture and urban planning from an architect-builder point of view?  I commence the introduction to this dissertation with a summary of the history of my lifelong interest in Aztec architecture and my professional and academic career in order to provide the context for the results of this research and to expose some of my personal biases as researcher and practicing architect in Mexico and Canada. I discuss concepts and ideas as to how and why Aztec cosmovision and religion were deeply embedded in Aztec architecture and urban planning. I present pictographic, written, oral, sculptural, archaeological, cultural, astronomical, mathematical, geometric and topographic notions that serve as a framework for the digital archaeoastronomical analyses of pre-Aztec and Aztec sites utilizing several applications. Based on these analyses, I reveal a set of design principles that were utilized in Aztec architecture and urban planning, and propose several innovative theories regarding the orientation of major Aztec sites in Central Mexico and the design principles embedded in the double temple teocalli, a unique Aztec building type. I also introduce a replicable methodology for archaeoastronomical analyses that can be utilized in any archeological site in the world.  Ever since I can remember, on February 5th, my family and I, together with all my paternal relatives, attended the celebrations of Nuestra Señora del Pueblito in Querétaro. For nine days, we danced, feasted and participated in ceremonies that went from the blessing of the sacrificial animals for the Día del caldo ([Beef] Stock Day) to the blessing of sugar figurines in the form of fruits that we would eat the last day of the feast. I recall the excitement when, after two hours cramped in our car full of relatives, food and clothes, we could see El Cerrito (Figure 1.1), a 2  small mountain that only the Elders were allowed to climb while the rest of us stayed in the plaza at the side of the mountain. I still remember the day when we followed them and discovered that the mountain had stairs to climb! The Elders did not see us at the time, but I will not forget the scolding we received after they found out. The following year, after the premature death of my father, Don Lucino, my grandfather asked me to go up the mountain with him. While we climbed up, sometimes on stairs, sometimes through loose pieces of rock, he told me that El Cerrito had been a temple for hundreds of years and had been visited by his family ever since he could remember. From that moment on, I saw El Cerrito with different eyes. As the years passed, I could distinguish portions of the temple that were still visible. I can still feel the awe of trying to understand how this temple was built.   Figure 1.1. El Cerrito (translated as "The Little Mountain") archaeological site in the state of Querétaro, Mexico. Except for some walls of the platforms and fragments of stairs, most of it remained uncovered until 1995, when excavations officially began.  Only the main façade has been partially restored (Photograph by Julià Sastre - CC-BY 2.0).  This awe stayed with me every time we went to archaeological sites and their on-site museums, or visited the Museo Nacional de Antropología (MNA), where I spent hours contemplating the model of the ceremonial precinct of Tenochtitlan. Since that time, I have searched for books about Aztec architecture but I always found the same image from the Museo Nacional de Antropología. The discovery of the Templo Mayor (Huey Teocalli) in 1979 increased my interest in Aztec architecture as I had heard for so many years that it was buried under the cathedral. 3  Years later, as a practicing architect, I understood the decision of the Conquistadores to construct the Cathedral beside the Templo Mayor; they utilized it as the source for construction materials. Many other buildings in the ceremonial precinct of Tenochtitlan suffered the same fate and traces of them can still be found in colonial edifices.  I frequently visited the excavations during the 1980s thanks to the friendship of my family with Pedro Ramírez Vázquez (the architect who designed the Museo Nacional de Antropología and later, the Museo del Templo Mayor), and read any information as soon as it was published. A myriad of articles and studies came out about the excavations, but never a publication about Aztec architecture that explored more than the Templo Mayor. The excavations of the Templo Mayor ignited an interest in Aztec architecture, and other archaeological sites such as Tlatelolco, received funding for excavation projects.  While I was in university, I had the privilege of attending the courses about Mesoamerican architecture imparted by architect Luis Mariano Aceves. His images and verbal descriptions of Teotihuacan were so vivid, that when I subsequently visited Teotihuacan, I could feel how spaces, buildings and mountains spoke to each other: architecture was the writing and the landscape was the canvas. Even though I had previously been in Teotihuacan many times, this was the first time I saw it with the eyes of an architect. Being one of the best students in the School of Architecture, several professors granted me the freedom to explore my interest in Mesoamerican architecture in Central Mexico, allowing me to study different aspects of it according to their subjects. I visited not only the sites within Mexico City, but also in the states of Mexico, Morelos, Puebla, Tlaxcala, Hidalgo, Querétaro, and even Veracruz. During these years, even though Aztec scholarship was producing a large amount of research, there was still none conducted on Aztec architecture other than the research related to the Templo Mayor. The only sources for Mesoamerican architecture that had a reference to Aztec architecture at that time were the Arquitectura Prehispánica by Marquina (1964), Ciudades precolombinas by Hardoy (1964) an the Pre-Columbian Architecture of Mesoamerica by Gendrop and Heyden (1973).  During my last two years in university, my family asked architect Pedro Ramírez Vázquez if I could join his architectural practice as an apprentice. I was really excited as it was one of the 4  most prominent firms in Mexico; its commissions not only included the Museo Nacional de Antropología and the Museo del Templo Mayor, but also numerous projects from museums, embassies, stadiums and international pavilions to the Basílica de Guadalupe (the most important Catholic temple for Mexicans). The agreement was that I would work as an unpaid intern every weekday afternoon until I graduated, by which time I would decide if I would stay in the firm.  On the first day, Don Pedro called me to his office. I nervously walked through the door into a relatively small office and found him sitting behind a beautiful wooden table that served as his desk. The white wall behind him only had a couple of shelves with books and some pre-Columbian figurines, but the wall on the opposite side had built-in bookshelves protected with panels covered by black and white images of some of his oeuvre. I was mesmerized when I saw images of the Museo Nacional de Antropología (MNA) and the tower of the Foreign Affairs Ministry in Tlatelolco with the archaeological remains in the forefront. At that moment, I was transported to the model of Tenochtitlan in the MNA and forgot where I was until I heard the voice of Don Pedro pronounce my name. What followed was a lively exchange about Mesoamerican architecture that lasted all afternoon. By the end of the conversation, he stood up, opened a discrete door to his right, and invited me to enter. This small door led, to my surprise, to an immense boardroom that had, along one wall, the most amazing collection of architectural and museography magazines; along the other perpendicular wall, bookshelves overflowing with architecture and art books; and on the opposite side, a floor-to-ceiling, wall-to-wall window with floating transparent shelves that held his glass artwork. He proceeded to ask me if I would like to help him with his personal library before I started to work in his studio. I immediately accepted as I could not keep my eyes off everything! The couple of years that followed were filled with rewarding conversations about architecture and museography, especially Mesoamerican architecture as we both shared the same passion. Every afternoon he would come into the boardroom and chat with me while he was working with his glasswork. This was also the first time I saw a book of old plans of Mexico City and facsimiles of codices that were not even in the collection of the university I attended.  5  The space in this introduction would be too small to recount what I learned from Architect Pedro Ramírez Vázquez about Mesoamerican architecture, archaeology, conservation and museography, but our conversations were fundamental for increasing my knowledge and interest about Aztec architecture.  All my plans changed at 7:19 AM on September 19, 1985 when an earthquake measuring 8.1 on the Richter scale shook Mexico City. In a matter of seconds, several parts of the city were destroyed. Hundreds of buildings collapsed and left thousands of people dead. A second earthquake occurred at 7:40 PM the next day. More devastation and destruction ensued and left many buildings heavily damaged. Our house had only a cracked wall, however as many other Mexicans, we slept on the streets in makeshift camps for the fear of having our homes fall on us. In the days that followed, we concentrated on helping find survivors in the rubble. A reporter described the scene in Mexico as similar to Beirut, which had been ravaged back then by the civil war in Lebanon. What followed was the most intensive reconstruction program in Mexico: the Programa de Renovación Habitacional Popular (Popular Residential Renovation Program), which eventually built 42 090 new homes, repaired 4 210, and rebuilt another 2 500 in 150 buildings listed as historical monuments. The program gained worldwide recognition for its size, efficiency and ability to bring together of many national and international organizations.  The reconstruction of the city meant a once-in-a-lifetime opportunity for many professionals (engineers, architects, and builders, among others) to construct or repair a large number of buildings (homes, schools, hospitals, etc.) in less than four years. I was no exception, as the father of one of my friends and civil engineer, recruited me to work as the Structural Engineering1 Coordinator of Zone 1 of the Programa de Renovación Habitacional Popular. The main responsibilities of my job were to determine if a building could be repaired or had to be demolished and to inspect the steel reinforcements before the concrete was poured into the structure. I spent most of my time on sites working alongside engineers and construction workers who had poured from all the surrounding areas of the Valley of Mexico. The first time I visited a                                                  1 Back in the eighties, the program of study of the School of Architecture at the Universidad Iberoamericana consisted of a set of six courses on structural engineering and six courses on construction science in addition to the regular design, geometry, theory and history of architecture courses, which resulted in a 5-year program plus a 1-year thesis. 6  site to determine the location of the foundations, I realized that most of the steel reinforcements were already on the ground. Concerned that it was done right, I asked for a steel measuring tape to check it. Nobody had one at that moment as the maestro (master builder) had left the site to buy sodas. To my surprise, I was handed over a stick with marks and a cord, and casually, one of the bricklayers asked me where I wanted to start. Fortunately, at that moment the maestro arrived and gave instructions to the bricklayers. When they were ready, the maestro took a measuring tape out of his pocket and I was able to confirm that the reinforcements were placed in the right place. When I asked the maestro about the stick and cord, he nonchalantly answered that those were all the tools they needed. From this moment on, I carefully observed how foundations and walls were laid with several tools complemented by sticks, cords, and mirrors. The use of the mirror took me a while to understand, until I saw its use to determine the location of a wall on a rather long lot. The coordination among the maestro, the construction workers and their varied tools fascinated me as they constituted a building construction entity that worked very efficiently.   When I read the descriptions of Sahagún about the skilled Aztec craftsmen, I could not help but think about the way I had seen the maestro work with his people, who were usually from the same family or small town. As many scholars have argued, the reconstruction, after the devastation caused by the Conquest, was only possible because the Aztecs had a building execution system that included skilled craftsmen, materials and tools.  After the Programa de Renovación Habitacional Popular, I started my architectural practice with another colleague. At the beginning, our commissions were mostly houses and small buildings, but in the early nineties, we landed the architectural supervision contract for the Mexican Foreign Trade Bank building in Mexico City. The architect was in Monterrey, a 1.5-hour flight from Mexico City, so he sent us the plans through long strips of paper via fax. I found the system inaccurate and time consuming, so I suggested we try sending diskettes via messenger services. This partially solved the problem, but making changes was still ineffective because we had to exchange diskettes, which also took time. Even though we finished the building before we effectively solved the matter, I became increasingly interested in Computer-Aided Design.  7  I searched for programs in several countries and I found the Masters of Advanced Studies in Architecture (MASA) with a specialization in Computational Tools in Design at the University of British Columbia. I traveled to Vancouver and met with Dr. Jerzy Wojtowicz. He accepted me without hesitation. He was impressed with my architectural design thesis not only for its content, but also because the text and plans had been done in a computer, which was not common at the time. It was a privilege to spend time in the studio with Dr. Wojtowicz as we had the most advanced computer systems and CAD programs in the world. Due to my interest in Mesoamerican architecture, and the expertise of Dr. Wojtowicz in geometry, he suggested I explore the geometry of the Templo Mayor. Since I already had a fair amount of material and the library had a quite complete collection of books and journal articles about the Templo Mayor, I decided to explore its regulating lines. I was intrigued by my findings, as I discovered relationships between the proportions of the building stages of the Templo Mayor as well as some key locations where offerings had been discovered. Technology enabled me to add as many layers of exploration as I needed. For my Master's thesis, I extended my findings and built the most accurate digital interpretation of the ceremonial precinct of Tenochtitlan within a multimedia application, one that allowed the user to explore different sources and display different interpretations according to the source.  Proud of my work, I traveled to Mexico to show my CD-ROM to Eduardo Matos Moctezuma, an icon in Mexican archaeology and the Director of the Templo Mayor Project and museum. To my dismay, Matos Moctezuma was unable to see me because his agenda was full for months. Sad but not defeated, I went to show my work to Architect Pedro Ramírez Vazquez whom I had also planned to visit during that trip. As always, Don Pedro received me with a lot of affection and patiently waited until I was ready to show him my work in the computer. The more I showed him, the more his small eyes opened. He was captivated with the interpretation and the technology, and kept on requesting that I show him more. At the end, he asked me, "Has Matos seen this?" I told him that he was unable to meet with me due to his lack of time. Don Pedro immediately activated the speakerphone and called the office of Matos at the Templo Mayor. The secretary transferred straightaway the call to Matos who was surprised to receive an unexpected call from Don Pedro. The conversation was short and to the point, and Matos agreed to see me the following morning. 8   Early the next day, I arrived at the Templo Mayor on time for the meeting, but was placed in a very small meeting room until Matos was able to see me. About a half an hour later, Matos finally arrived. Without much conversation, I started to show him my CD-ROM. His reaction was very similar to that of Don Pedro; the more I showed him, the more he wanted to see. However, when I showed him the plan of the ceremonial precinct he told me in a slightly louder voice, "Stop." He looked at me and asked, "How did you know that the ball court was in that location if we only discovered it in the last few weeks and have not shared our findings with anybody?" I immediately explained that I had utilized geometric and achaeoastronomical principles to determine its location. He was so astonished that he asked me to go to his office so that Dr. Leonardo López Luján could also see the CD-ROM and hear my interpretation. Again, I received a similar reaction from López Luján who asked the secretary to call the archaeologists working on-site to come to a larger meeting room to see my work. Everybody was fascinated with the media and the interpretation. Even though it was a great academic achievement for me as it validated my architectural research methodology, the results of my Master's thesis encouraged me to continue researching Aztec architecture, as it was an aspect of Aztec culture that was still not being addressed by scholars except for research directly related to the Templo Mayor.  The years that followed were so full of activity and went by so rapidly—I started both a doctorate and a family—that as I now reflect upon them they seem more dreamlike than real. During those years, I continued my research but got increasingly involved in the continuous development of digital tools and the internet in all areas of academia. My technical expertise was sought after because I could move fluidly from discipline to discipline and from paper to technology. I also became more involved with the Indigenous community, who had always been a source of encouragement and support since I came to UBC.  This relationship validated my Indigenous heritage in many ways. We not only shared cultural practices, but I was introduced to post-colonial theories. I had the opportunity of sharing discussions with Māori educators and scholars Dr. Linda Tuhiwai Smith and Dr. Graham Hingangaroa Smith, as well as spending time almost every day with Dr. Jo-ann Archibald (Q'um 9  Q'um Xiiem) due to my role at the First Nations House of Learning. The validity of Indigenous knowledge in my own research was strengthened when was I was invited as the visiting scholar of the James Henare Māori Research Centre at The University of Auckland by Dr. Te Tuhi Robust. I shared research with scholars and community members throughout northern New Zealand, however it was the oral history embedded in their architecture that stayed with me. After my time in New Zealand, many of the stories from my Elders came back to me. I could see Doña Josefa talking to my uncles while we sat down quietly in the corner of her house. It was built on a temple, or so they said. Hence, local history became an additional source in my research about Aztec architecture.  Research Methodology  In order to answer my research question I utilized what could be best described as a radial methodology where Aztec architecture and urban planning where always at the centre of all the investigations I made in the different disciplines: archaeology, art, history, astronomy, geography, geometry, mathematics and religion. This approach also resulted in my applying different architectural research methodologies in each chapter depending on the source material and the expected results.  Hence, I analyzed ethno-historical sources following an interpretative-historical research approach with the aim of defining Aztec typology, understanding the relationships between Aztec cosmology and architecture and exploring Aztec mathematics, geometry and topography. However, to analyze the topography and the movement of the Sun in each site with the precision I intended, I followed a more scientific approach in the archaeoastronomical-topographic analyses chapter that would let the archaeological sites reveal their design principles. To this end, I developed a detailed step-by-step methodology, applied it to the archaeological sites and summarized the findings by comparing the same kind of data among the sites. The results of this approach not only answered my research question but brought forth theories that contribute and enrich current Aztec and Mesoamerican scholarship.  10  Chapter One, the introduction, is a synthesis of how my research has come together. It begins with the research question and continues with a summary of the history of my lifelong investigation into Aztec architecture and my professional and academic careers in order to provide the context for the results of this research.  Chapter Two is an overview of the different ethno-historical, archaeological and sculptural sources where architectural representations are present either in pictorial, written or physical form. The first section presents a review of Aztec historiography after the Conquest. The subsequent sections include a description of each source and a summary of the architectural and urban depictions found within the source. These sources include: pictorial manuscripts, pictorial-administrative manuscripts, eyewitness accounts of the Conquistadores, chronicles compiled by the missionaries, archaeological evidence in pre-Aztec sites, archaeological evidence in Aztec sites, monumental sculpture, as well as architectural and urban models.  Chapter Three presents a visual sample of the inventory of Aztec architectural types that was done for this research based on the meticulous analyses of the ethno-historical sources carried out in Chapter 1 in order to investigate the common features of each architectural type, especially of the double teocalli, which is considered the most distinctive architectural type. To this end, the first section introduces the concept of typology following the ICOMOS Principles for the Recording of Monuments, Groups of Buildings and Sites and discusses the role of typological studies within the context of architectural research in Latin-America. The second section argues the need to define Aztec building types within their cultural context, which serves as the antechamber for the third section that consists of a representative sample of  probably the most thorough inventory of Aztec building types in Aztec scholarship. Each sub-section presents a dossier of each building type following ICOMOS principles. The fourth and last section discusses the application of the urban planning principles of Tula and Teotihuacan in the design of Tenochtitlan.  Chapter Four introduces the Aztec cosmological concepts of space and time in order to understand how they were embedded in Aztec architecture and urban planning, as the research carried out in the ethnohistorical sources (Chapter 2) and the typological studies (Chapter 3) 11  revealed their intrinsic connections. The first section presents the concept of cosmovision and its relationship with the landscape, skyscape and religious beliefs embedded in the symbolism of the Huey Teocalli. The second section narrates two fundamental stories in Aztec religion and mythology: the creation of the world and the birth of Huitzilopochtli —god of Sun, fire, war and patron deity of the Aztec— and the relationship of these myths with the four directions, the movement of the Sun across the sky and the symbolic meaning of mountains. The third section describes the concept of space and time in the Aztec calendar. The fourth section describes how these cosmological concepts were integrated into the sacred landscape comprised of mountains, caves and bodies of water, and emphasizes the importance of Tlaloc — god of rain, water and lighting— and the rituals performed on Cerro Tlaloc. The last section introduces the research carried out in the field of high mountain archaeology and its relevance for the understanding of the sacred landscape in the Valley of Mexico.  Chapter Five provides an overview of Aztec astronomy, mathematics and geometry with the purpose of understanding how these disciplines were applied to Aztec architecture and urban planning, as this knowledge was necessary to create the horizon reference system to track the Sun at calendrically significant intervals within the solstitial points as presented in Chapter 4 and to construct their cities and buildings. To this end, the first section includes an explanation of archaeoastronomy, and its foundations and application in the study of archaeological sites; is followed by an overview of Aztec astronomy; and concludes with a technical explanation about charting the movement of the Sun. The second section introduces Aztec mathematics, including a discussion of numerical systems that included linear and angular measuring systems. The third section presents Aztec geometry and the underlying design principles within sculpture and architecture that were undoubtedly applied to architecture and urban planning. The last section presents an overview of Aztec building practice —including designers, tradesmen, materials and tools recorded in historical and linguistic sources— as a sophisticated design and construction system was required to lay out their urban centres and architectural structures.  Chapter Six has two main sections. The first is a step-by-step description of the methodology I developed to analyze each site, as a very dissimilar corpus of information had to be taken into consideration: from religious myths, to technical information distinct for each location (its Sun 12  path, rising and setting times of the Sun during the year, and altitude and azimuth of the Sun in a certain day), to the topographic features such as mountains, caves and springs. The second section includes the archaeoastronomical-topographic analyses of two pre-Aztec sites —Teotihuacan and Tula— and five Aztec sites —Tenochtitlan, Tlatelolco, Tenayuca, Santa Cecilia Acatitlan and Teopanzolco. The analyses of each of these sites consists of four parts: a historical background; a summary of previous archaeoastronomical research and theories that have been proposed to explain its orientation; a discussion of the digital archaeoastronomical analyses and research findings; and a selection of images to illustrate the analyses.  Each archaeoastronomical analysis involved identifying the site in the context of the Valley of Mexico, defining the major alignment of the site, calculating the visibility of major topographic features, exploring with precision each significant direction (site alignment, solstices and equinoxes), building an horizon calendar based on identified alignments, and summarizing the findings of each site. These summaries contain the same type of information that allows the comparison among sites and the identification of their similarities and differences. The chapter concludes with a set of the main design principles of Aztec architecture and urban design deduced from my research.  Chapter Six is the centre of the radial methodology where all the cultural information extracted from traditional and non-traditional ethnohistoric sources converges and overlaps in order to understand the design principles of Aztec architecture and urban planning; the research carried out in the previous chapters demonstrated that cultural aspects such as religion, astronomy, mathematics and geometry were embedded in their urban centres and architectural structures. This chapter is divided in two main sections. The purpose of the first section is to demonstrate  with a case study the methodology that was applied in the archaeoastronomical analyses through a series of images and detailed explanations. This methodology is described step-by-step, as a very dissimilar corpus of information — that ranged from religious, mathematic and geometric cultural knowledge to specific topographic and solar information distinct to each location— had to be taken into consideration. The topographic and solar information included: the seasonal-and-hourly positional changes of the Sun throughout the year; the  rising and setting times of the Sun during the solstices, equinoxes and alignment dates; the altitude and azimuth of the Sun these dates; and finally, the topographic features in the local horizon of each site such as mountains, caves and springs. The second section is a summary of the archaeoastronomical-topographic 13  analyses of two pre-Aztec sites, Teotihuacan and Tula, and five Aztec sites: Tenochtitlan, Tlatelolco, Tenayuca, Santa Cecilia Acatitlan and Teopanzolco. The analysis of each of these sites has four parts: a historical background; a summary of previous archaeoastronomical research and theories that have been proposed to explain its orientation; a discussion of the digital archaeoastronomical analyses and research findings; and a selection of images to illustrate the analyses.  The archaeoastronomical-topographic analyses of each site consists of: identifying the site in the context of the Valley of Mexico, defining the major alignment of the site, calculating the visibility of major topographic features, exploring with precision each significant direction (site alignment, solstices and equinoxes), building an horizon calendar based on identified alignments and summarizing the findings of each site. These summaries contain the same type of information that allows the comparison among sites and the identification of their similarities and differences. The chapter concludes with a discussion of the main urban and architectural design principles deduced from the archaeoastronomical-topographic analyses and their application in main Aztec cities and their respective Huey Teocallis.  Chapter Seven, the conclusion, is structured in four parts. The first part synthesizes the contributions of each chapter and integrates them into the key architectural and urban findings of this research. The second part identifies the implications of the research findings in Mesoamerican and Aztec scholarship. The third part discusses the benefits and limitations of utilizing digital resources and applications for this type of interdisciplinary research. The last part outlines further research that can be performed utilizing this methodology in Aztec sites or other archeological sites around the world. 14  Chapter 2: Sources for the Study of Aztec Architecture and Urban Planning  2.1 Introduction   The aim of this chapter is to give an overview of the different ethno-historical, archaeological and sculptural sources where architectural representations are present either in pictorial, written or physical form. The first section presents a review of Aztec historiography after the Conquest. The subsequent sections include a description of each source and a summary of the architectural and urban depictions found within the source. These sources include: pictorial manuscripts, pictorial-administrative manuscripts, eyewitness accounts of the Conquistadores, chronicles compiled by the missionaries, archaeological evidence in pre-Aztec sites, archaeological evidence in Aztec sites, monumental sculpture, as well as architectural and urban models.  2.2 Overview of Aztec Historiography  The understanding of Aztec historiography is a complex endeavor, as the hybrid nature of the primary sources is as diverse in format and content as the historical context in which they were created and transmitted. Scholars such as León Portilla (1971) and Glass in collaboration with Robertson and Nicholson (1975), among others, have aided in the understanding of these sources by proposing different classifications for the vast body of historical material. However, Santamarina (2006:261) has demonstrated that a multitude of classifications2 can be established based on the system of representation (pictorial or alphabetical), language (Nahuatl, Castilian or Latin), thematic character (historical-political, religious, ethnographic, economic), ethnic or professional origin of the author (native, mestizo, Spanish, or conquistador, clergyman, official), or origin of the primary source (native pictographs, oral tradition, accounts), to name a few. The dating of the sources (pre-Hispanic or colonial) in particular has caused real disagreements among scholars who base most of their arguments on the iconographic analysis of the drawn                                                  2 The intent of Santamarina is not to propose additional or more detailed classifications systems of ethno-historical sources, but to demonstrate its heterogeneous character. Even though some sources could be placed in a single category, most of their (sources) could fall into several categories, which is a reflection of the acculturation process that occurred during the early colonial period (2006: 262).  15  elements (Mohar 1997:56). Therefore, any classification of historical sources about the Aztecs has the potential of being controversial.  In addition, it is important to point out that Aztec historiography began with the Aztec themselves, as ethno-historical sources reveal that the rulers of Tenochtitlan performed archaeological excavations in both Teotihuacán and Tula with the purpose of legitimizing their ancestral rights to power and sources of Aztec identity (Smith 2008a:25). These cultures inhabited the Central Highlands of Mexico and its surroundings several centuries before the Aztecs arrived to the valley. Teotihuacan was established in 150 B.C. and was destroyed around A.D. 650, its hegemony lasting for more than eight centuries. The political and commercial void left by Teotihuacan was filled by Tula from 700 to 1150 A.D. For the Aztecs, Teotihuacan was the place where time began and Tula was the source of power. Since Tula had claimed for itself the role of the mythical Tollan, the Aztecs justified their right to military expansion due to their Toltec heritage (López Austin and López Luján 2001:199). The Aztecs considered the Toltecs as their ancestors and utilized Tula and Toltec practices as the basis for much of Aztec religion (Evans 2004:402).  Except for the research done by Smith in Aztec City-State Capitals, the few studies of Aztec architecture (Marquina 1964, Matos 1999, Pasztory 1983, Aguilar 2007) have mainly concentrated on its physical description, its archaeological characterization (such as belonging to certain cultural and temporal horizons), the exaltation of its physical characteristics, the analysis of certain features, and in some cases, proposing visual interpretations. Hence, a different approach to Aztec historiography is necessary that focuses on Aztec architecture from an architectural point of view rather than from a political, economic, social, cultural or religious point of view.  16  Consequently, I propose a classification of primary sources that utilizes the categories suggested by León Portilla3 as a basis for the organization of material, since he has attributed the same value to ethno-historical and archaeological evidence throughout his oeuvre:  It is necessary to insist on the importance for the historian of pre-Hispanic cultures to know, as widely and deeply as possible, the results of archaeological research. Studies of primary sources such as codices, texts by indigenous writers, and by Spanish chroniclers, take on new meaning and can be placed in its corresponding historical time when they are associated with archaeological discoveries.  It is only by considering the written sources and archaeology as two forms of knowledge that must converge at one point, will it be possible to penetrate more and more into a culture where much remains to be elucidated (León Portilla 1971:40).4  This classification was complemented by the wide corpus of historiographical and archaeological research about the Aztecs carried out by Mexican and foreign scholars which has often gone in different directions. According to Drinot, there is awareness that:  this divergence is a reality in Mexican historiography since much of USA-based Mexican historiography has become largely self-referential. At its most extreme, this process amounts to a form of academic colonialism. Mexico serves as a source of raw material which USA based historians mine assiduously. However, the historiography that results serves to feed academic debates within USA universities but is seldom intended to                                                  3 A summary of this classification can be found in De Teotihuacan a los Aztecas: Antología de Fuentes e Interpretaciones Históricas (León Portilla 1971:29-50).  4 Translated from León Portilla (1971:40):  No es necesario insistir en la importancia que tiene para el historiador de las culturas prehispánicas conocer, tan amplia y profundamente como le sea posible, los resultados de la investigación arqueológica. Los estudios acerca de las otras fuentes primarias, los códices, los textos indígenas y de los cronistas españoles, adquieren un nuevo sentido y pueden situarse mejor en su correspondiente momento, al ser relacionados con los descubrimientos arqueológicos. Tan solo así, considerando a las fuentes escritas y a la arqueología como dos formas de conocimiento que deben convergir sobre un mismo punto, será posible penetrar cada vez más en un mundo de cultura sobre el que tanto queda por esclarecer.  17  influence the writing of Mexican history in Mexico, though it may unintentionally do so (Drinot 2000:72).  In spite of this divergence, I have employed the studies that best inform the architectural subject matter. This corpus included the original primary source as well as its distinct and sometimes conflicting interpretations.  This historiography was expanded to include monumental sculpture, urban and architectural models and oral tradition as categories. Paradoxically, in spite of the evident geometric characteristics in the creation of sculptural pieces, studies have concentrated on descriptions of its religious, iconographic and its epigraphic characteristics. Furthermore, urban and architectural models have barely been studied (Schávelzon 2004).  18    Figure 2.1. Classification of Primary Sources.  Sources for the Study of Aztec Urban and Architectural Space Pictorial Manuscripts Ritual-calendrical Historical Economic Cartographic Administrative Written Manuscripts Eyewitness Accounts by the Conquistadors Chronicles Compiled by the Missionaries Writings by Indigenous and Mestizo Authors  Archaeological Evidence Archaeological Remains in Pre-Aztec Sites Archaeological Remains in Aztec sites Archaeological Records Monumental Sculpture Urban and Architectual Models Oral Tradition 19  It should be emphasized that the proposed classification of primary sources for the study of Aztec urban and architectural space (see Figure 2.1) does not intend to cover the extensive body of ethno-historical material contained in the work of several scholars such as León Portilla, in the Guide to Ethno-historical Sources of the Handbook of Middle American Indians or in the Códices y Pinturas Tradicionales Indígenas en el Archivo General de la Nación: Estudio y Catálogo, but only the main published sources5 where architectural manifestations were present.  These primary sources must be interpreted critically, as their purpose was not to provide a precise account of the past, but to serve the interests and motivations of the groups that participated in them. They are valuable for understanding Aztec architecture and thought even though the use of these sources to understand Aztec culture is problematic because of obvious biases due to Spanish influence and the specific native source which "leads us to know more about the life and ideology of the aristocracy rather than about common people, and more about religion than about any other aspect of life" (Pasztory 1983:33).  After the conquest, interpretations of these primary sources began to emerge when the objects, animals, and even Indigenous people began to arrive from the Colonies to European capitals. This caused a great impression among scholars who became increasingly interested in the New World and began to include this material in their work. They were particularly fascinated with Tenochtitlan, and by 1576, interpretations of the ceremonial precinct were already included in the Civitates orbis terrarum pictorial atlas of Georgius Braun and Franz Hohenberg, which contributed to the dispersal of the fame of the capital of the Aztec empire (Boone 1987:11). In 1590, José de Acosta used information provided by Juan de Tovar, who in turn copied either Diego Duran's Historia (finished in 1571 but not published until 1867-80) or the Crónica X, the lost prototype for much of Duran's history to introduce a distinct description of the ceremonial precinct in his Historia natural y moral de las Indias. The Belgian engraver Théodore de Bry and his sons (Figure 2.2) included a portion of the descriptions of Acosta in their volume of the                                                  5 Besides the material contained in the Guide to Ethno-historical Sources of the Handbook of Middle American Indians, there is a large collection of manuscripts housed in the Archivo General de la Nación that was collected in the Códices y Pinturas Tradicionales Indígenas en el Archivo General de la Nación: Estudio y Catálogo under a 15-year project lead by Galarza initiated in 1980. Besides a scant catalog, this material has not been published or analyzed.  20  Grands Voyages series, but accompanied it with a "wildly fanciful" engraving of the Templo Mayor in 1601 (Boone 1987:13).   Figure 2.2. Engraving of the Templo Mayor by Théodore De Bry, published in 1601 to illustrate the history of José de Acosta (Boone 1987: Figure 6).  In New Spain, Franciscan friar and historian Juan de Torquemada ignored the work done by Acosta and de Bry and synthetized material taken from López de Gómara, Motolinía and Sahagún6 for the description of the ceremonial precinct and the deities worshipped in the main temple in his Monarchia Indiana in 1601. After Torquemada, the work of Sahagún was not considered in subsequent histories that were written during the seventeenth and eighteenth centuries (Boone 1987:14). In contrast, Antonio de Solís, a Spanish historian who was chronicler of the Indies from 1661 to 1686, based his depiction and engraving of the ceremonial precinct (Figure 2.3) on the account of Antonio de Solís that he included in his Historia de la Conquista de México, Población y Progresos de la América Septentrional, Conocida con el Nombre de Nueva España published in 1684 (Boone 1987:14). The engraving of Antonio de Solís became                                                  6 Even though the Historia General de las Cosas de la Nueva España compiled by Sahagún from 1575-80, "was not fully published until 1829, his view of the Templo Mayor, including his list of the seventy-eight temples of the ceremonial precinct were known by some scholars in manuscript and entered the published literature early" (Hill Boone Templo Mayor Research, 1521-1978: 14). 21  the basis for numerous illustrations that were made for almost a century until the publication in 1780-81 of the multi-volume Storia Antica by mestizo historian Francisco Javier Clavijero. In his description of the ceremonial precinct, he combined the work and illustrations of several historians and accounts of Conquistadors, which he accompanied with an engraving of the Templo Mayor (Boone 1987:16).   Figure 2.3. Engraving of the Templo Mayor, published in 1684 to illustrate the history of Antonio de Solís (Boone 1987: Figure 7).  The literary approach to history that had prevailed since 1521 was transformed by the discoveries of 1790. In fact, scholars who have written about the history of archaeology in Mexico, agree that systematic studies about Aztec culture began when the Aztec Sun stone and the Earth Goddess Coatlicue were discovered in 1790 under the Plaza de Armas, the main plaza in the centre of Mexico City, where extensive public works were ordered by the Spanish viceroy, Juan Vicente de Güemes Pacheco de Padilla y Horcasitas, second count of Revillagigedo (Matos Moctezuma 1979:10). The viceroy, who had experienced the urban renovation of Madrid, decided to transform the insecure, chaotic and insalubrious Mexico City, into a more habitable city. He gave the responsibility to Ignacio de Castera, a Spanish architect and urban planner, who initiated various public works projects throughout the city including the widening of the streets, the construction of bridges and avenues, the installation of water supply and sanitation systems, 22  and the remodeling of the Plaza de Armas. This activity yielded the unexpected result of accidentally unearthing many monuments and archaeological artifacts from pre-colonial times (López Luján 2001:72). Many of these were drawn by the Spanish Captain Guillermo Dupaix in his Descripción de Antiguos Monumentos Mexicanos in 1794 (Figure 2.4), which is considered an invaluable document of the archaeological findings during the tenure of Revillagigedo at the end of the eighteenth century (López Luján 2001:81).    Figure 2.4. Front page and monuments number 8 and 19 in the Descripción de Antiguos Monumentos Mexicanos by Guillermo Dupaix (López Luján 2001:  Figures on pages 72, 74 and 79).  These accidental discoveries also marked an attitude change towards the Aztec past. They were not only meaningful as monumental reminders of the Aztec past, but the decision of the authorities and the clergy to keep them was unusual (Manzanilla and López Luján 2001:322). Instead of destroying them, the Spanish viceroy Revillagigedo, ordered their protection and preservation and studies about them began to emerge. Antonio León y Gama, an astronomer, made the first studies of the Aztec Sun Stone and the Coatlicue. His Descripción Histórica y Cronológica de las Dos Piedras (Historical and Chronological Description of the Two Stones) is the first study that took an archaeological monument as a source to explain a "system of ideas;" 23  in this case, the calendrical and chronological conception of the Aztec articulated in the hieroglyphics (Florescano 1997:151).   Between 1780 and 1810, the criollos’ interest in investigating their Indigenous past through material evidence that had survived the Conquest received extraordinary support from the Spanish authorities influenced by the ideas of the Enlightenment or the Age of Reason, which stimulated the archaeological excavations of Palenque from 1784 (Florescano 1997:152). The valuation of the archaeological and documental testimonies served as sources to comprehend the old Indigenous cultures. The criollos searched for an identity in their pre-Columbian past that was revived after the Independence of Mexico from Spain in 1821. The reintegration of the dismembered history of the country and the reconstruction of its past became central objectives for creating the identity of the new Mexican Republic (Florescano 1997:152). Scholars expanded their understanding of the past by interpreting the archaeological findings and complemented their scholarship with the publication of the works of Durán, Sahagún and the codices illustrated by Kingsborough that were made public during the time of Independence. Alfredo Chavero identified Coatlicue as the Earth goddess by employing documental testimonies in 1888. Discussions and studies proliferated about the precise location of the Great Temple, its appearance and the ceremonies performed in it.  The Museo Nacional (National Museum) experienced great development in all its areas and functions between 1876 and 1910. The research, teaching and diffusion functions expanded during this period, and in 1877 the museum undertook the first archaeological investigation in Oaxaca and another one in Cempoala in 1890 (Florescano 1997:158). The museum became the national centre of historical and anthropological research and acquired an international reputation under the leadership of Francisco del Paso y Troncoso (1889-1890 and 1892-1910). In 1900, Leopoldo Batres carried out the first official archaeological excavation in Mexico City after workers found archaeological remains when they began to build a sewer behind the Cathedral. Even though he had no training in archaeology, he recorded his findings with drawings (Figure 2.5) and pictures that he eventually published in his book Exploraciones Arqueológicas en las Calle de Escalerillas (Explorations in the Escalerillas Street) (Matos Moctezuma 1990:23).  24   Figure 2.5. Plan of the ceremonial precinct and the Templo Mayor by Leopoldo Batres published in 1902 (Boone 1987:Figure 26).  In the period between 1910 and 1920, the social unrest and the political restlessness that fostered the revolutionary process introduced new characteristics to Mexican nationalism (Florescano 1997: 165). In 1917, Manuel Gamio, a former student of the Museo Nacional and the first Mexican who made specialized studies abroad, took advantage of the disruption that the Revolution generated, made several original propositions that would define a new cultural approach for the nation and set the foundations for the Indigenismo project. Gamio suggested the need for a new aesthetic that rejected Western Canons and valued the Indigenous creations under the framework of its own historical and cultural categories. When he projected this vision, he created programs that combined the anthropological interest in Indigenous populations with the decision to improve their situation and integrate them to the national development underway (Florescano 1997:166). Gamio was also the first to apply stratigraphic archaeology methods when he excavated a site one block northeast of the cathedral. This excavation led to the discovery of the southwestern section the Templo Mayor. Boone describes his findings:  25  There he found a monumental serpent head at the base of a west-facing balustrade flanked by stairways, as well as a pyramidal nucleus of three stages and several superposed floors, which he recognized as representing various building phases. In addition, he uncovered more than five hundred objects, including two colossal masonry braziers on either side of a stone cist containing a cache of skulls, as well as stone merlons in the shape of shells, polychrome relief slabs carved with warriors, tenoned stone skulls and serpent heads, small idols, sherds, mica, and copper pyrite (Boone 1987:43).  This discovery revitalized the debate regarding the location of the Templo Mayor that had commenced with the studies made by Chavero, Seler and Batres. As a result of this finding, various scholars in Mexico and Europe, including Alfred Maudslay, Roque Ceballos Novelo and E. Guillemin-Tarayre, devoted many studies to this matter. Subsequent years were marked by accidental discoveries as a result of public or private works in downtown Mexico City (Boone 1987:45).  Throughout the post-revolutionary period, numerous other Aztec and Central Mexican sites were explored. Archaeologists continued excavating Teotihuacán through the 1930s, explored Tizatlán and Teopanzolco in the 1920s, Tenayuca in the 1920s and 1930s, Malinalco in the 1930s, Tula in the 1940s and Tlatelolco in the 1940s and 1950s (Boone 1987:48). Each discovery and subsequent study added material to the debate of the size and location of the ceremonial precinct of Tenochtitlan. Further findings were made in the mid-1960s and early 1970s in scattered excavations made during the repairs of several colonial buildings and during the construction of the subway. These included the temple dedicated to the wind god Ehecatl-Quetzalcoatl and other kinds of structures, such as small painted shrines with forecourts and circular base temples. These were soon interpreted and more studies were published.  26  This all changed when the accidental discovery of the Coyolxauhqui7 led to the excavation of the Templo Mayor in 1978 (Figure 2.6). This massive archaeological excavation soon became the focus of the nation when the economy was disintegrating and the sense of national identity needed reinforcing. The Templo Mayor excavations, and those that followed such as the Programa de Arqueología Urbana (Urban Archaeology Program), benefited from the substantial support of the then President José López Portillo and of subsequent Presidents. Since the discoveries of 1978, the group in power has continuously provided the financial patronage needed for these excavations, which have often been utilized to legitimize their political agenda and further their economic interests. Furthermore, these excavations rekindled the interest in Aztec culture; and hundreds of studies have been completed by Mexican and foreign and academics.   Figure 2.6. Discovery of the Coyolxauhqui in 1978 (Photograph by Rescate Arqueológico-INAH).  Current studies about Aztec culture come from several disciples: anthropology, history, art history, religion and literature. Aztec culture provides a gateway to Mesoamerican studies for Central Mexico because it "represents the connecting point between the pre-Hispanic past and the globalized present" and "international attention continues to focus upon the ongoing                                                  7 Up to six representations of the Coyolxauhqui have been identified, but the monolith found in 1978 is the only complete full-body depiction of the goddess (Matos Moctezuma 1991:24). 27  excavations at the Templo Mayor" (Nichols and Evans 2009:265). Research has become interdisciplinary and now comprises subjects that range from the environment to the economy, politics, social relations, ideology and interregional relations (Nichols and Evans 2009:265).  The Instituto Nacional de Antropología e Historia, INAH (National Institute of Anthropology and History) has continued excavating several Aztecs sites and carrying out research about Aztec culture. This research corpus has been supplemented by several books about Aztec art, archaeology, and ethnohistory (Nichols and Evans 2009:265). It has also been accompanied by major international exhibitions sponsored by foreign companies involved in the tourism, energy, and resource industries in Mexico: the 2008 exhibition The Aztec World at The Field Museum in Chicago was funded by Exelon, the largest energy provider in the United States; the 2009 exhibition Moctezuma: Aztec Ruler at the British Museum was sponsored by Mexicana, a Mexican airline company and ArcelorMittlal, the largest steel producing company in the world; and the 2010 exhibition The Aztec Pantheon and the Art of the Empire at the Getty Villa was organized by INAH and the J. Paul Getty Museum after it had to return a considerable number of objects from its Roman and Greek collection obtained through the illegal international antiquity market.  2.3 Pictorial Manuscripts  Few pre-Hispanic pictorial manuscripts survive. Most were burned by the Spanish authorities and the missionaries in their zeal to obliterate Aztec beliefs. However, the church also commissioned missionaries to research Aztec customs and religion for their conversion, so many old books were copied and chronicles were illustrated by native artists.8 While some were probably replicas of the originals, their style began to change after they learned European illustration techniques and integrated "realistic drawing, perspective, light and shade, and other elements of western art" with their native style (Pasztory 1983:179). This style consisted of Aztec and Mixtec traditions that utilized similar pictorial conventions, which enabled them to communicate. These conventions integrated representational, ideographic and phonetic                                                  8 The Handbook of Middle American Indians lists hundreds of these documents that survived in Mexican and European archives. 28  components, and facilitated the exchange between Postclassic cultures. The form of the pictorials followed their content and function (Boone 200b:39-61), hence they are a valuable source for the study of Aztec architecture.  Even though codices have been studied as a literary genre (León Portilla 1992) and as an intellectual, documentary, and pictorial genre (Boone 2000; Johansson 2004), they have not been analyzed from an architectural-urban point of view. Therefore, these sections include the meticulous analysis that was performed in each original source. Until this material became available in the past years, this analysis would not have been possible as neither the original documents nor their facsimiles had the high resolution of the digitized artifacts.   Hence, the dossier of each document consists of a description and content of the sources as well a summary of architectural and urban depictions identified by this research. The results of this material were later utilized to compile the inventory of Aztec building types.  2.3.1 Codex Aubin  Description The Codex Aubin (15.5 x 13.4 cm, 81 leaves)9 is a historical manuscript that records events from the years 1168-1591 and 1595-1596 with an addition for 1597-1608, through images and descriptions written in Nahuatl (Glass and Robertson 1975:88). The codex begins with the departure from Aztlan in 1168 and ends with the arrival of a new viceroy and archbishop in 1607-1608 (Leibsohn 2006).  Content  The codex is divided into a main account and an appendix. The main account is comprised of three sections that depict the migration from Aztlan to Tenochtitlan, the imperial history of Tenochtitlan and colonial events. The key events recorded in this section are "the New Fire ceremony at Coatepec, the Mexica defeat at Chapultepec, the founding of Tenochtitlan, the                                                  9 Measurements according to the description from the British Museum database. 29  installation and deaths of imperial tlatoque, enlargements of the Templo Mayor, comets and eclipses, the arrival of Spaniards, deaths from smallpox, local building projects and changes in altepetl leadership" (Leibsohn 2006). The appendix lists rulers from Tenoch through 1607 (Glass and Robertson 1975:89). The codex currently resides in the British Museum, although there are several copies and partial translations made in the nineteenth and twentieth centuries that are currently in collections in Europe and Mexico (Figure 2.7).  Summary of Architectural and Urban Depictions The architectural depictions include single temple pyramids (plates 035-036_22v, 035-036_26r, 035-036_37v, 035-036_38r), double temple pyramids, a tzompantli (035-.36_11v), temazcal (035-036_24r , 035-036_24rv) and a view of the ceremonial precinct of Tenochtitlan (035-036_41v).    (a) (b)  Figure 2.7. (a) Calendar, folios 2v and 3r; (b) Departure from Aztlan, each group is represented as a house glyph, folio 4r, Codex Aubin (British Museum, CC-BY-NC-SA 4.0).  30  2.3.2 Codex Azcatitlan  Description The Codex Azcatitlan (21 x 28 cm, 25 leaves) is a historical manuscript that chronicles Mexican history since their departure from Aztlan (Azcatitlan) and Colhuacan in 1168 to the Spanish Conquest and early colonial period (Glass and Robertson 1975:88).  Content  The codex is divided into three sections: the migration from Aztlán to Tenochtitlan and Tlatelolco; the rulers of Tenochtitlan from Acamapichtli to Motecuhzoma II Xocoyotzin, with their conquests and other important events of their reigns; and, in the final pages, the Spanish conquest and the early Colonial period. The key events recorded in the first part of the codex are the myth of Huitzilopochtli's birth and the battles of Chapultepec, Xochimilco and Colhuacan; the founding of Mexico; and the coronation of the first rulers of Tenochtitlan and Tlatelolco. The second part of the codex includes several conquests and other events such as plagues, the 1507 New Fire ceremony and the construction of important buildings. The last part of the codex depicts three incomplete scenes of the Spanish conquest, the meeting between Motecuhzoma II and Cortés, the battle scene where Motecuhzoma died, as well as the siege of Mexico (Graulich 2006). The codex currently resides in the Bibliothèque Nationale de France (Figure 2.8).  Summary of Architectural and Urban Depictions The architectural depictions include single temple pyramids (plates 059-064_02, 059-064_03, 059-064_05, 059-064_10), double temple pyramids (plates 059-064_06, 059-064_18, 059-064_19, 059-064_20, 059-064_21, 059-064_22, 059-064_24), circular temple pyramids (plate 059-064_07), and tzompantlis (plates 059-064_08, 059-064_22).  31   Figure 2.8. Departure from Aztlan, Codex Azcatitlan, folio 2 (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0).  2.3.3 Codex Borbonicus  Description The Codex Borbonicus (39 x 40 cm, 36 leaves) is a ritual-calendrical pictorial manuscript that is notable for "the insight it provides into Aztec rituals centered on two ancient Mesoamerican calendric constructs," the 260-day ritual calendar and the solar-based 365-day calendar (Quiñones 2006). The dating of this codex has been the object of much controversy, as E. T. Hamy, M.A. Aubin, E. Seler, G. Valliant and Alfonso Caso consider it pre-Hispanic while Nowotny and Robertson believe it is Post-Conquest (Mohar 1997:59).  Content  The codex is divided into four sections (two major and two minor). The first section is a tonalpohualli or divinatory calendar of 260 days used to calculate the fate of a given day, with each plate containing the presiding deity flanked by two sets of smaller boxes. The first set contains the images of 13 of the 20-day signs and the numerals 1 to 13 which share space with 9 Night Lords; the second set encloses another set of 13 day lords with 13 associated flying creatures. The second section illustrates the association between the 9 Lords of the Night with each assigned day for a period of 52 years. The third section is the festive calendar that consists of 18 months of 20 days each and their corresponding ceremonies. The final section repeats an unfinished period of 52-years, (incomplete because of the loss of the last two panels) and 32  indicates the next New Year ceremony (Quiñones 2006). The codex currently resides in the Bibliothèque Nationale de France (Figure 2.9).  Summary of Architectural and Urban Depictions The architectural depictions include single temple pyramids (plates 15, 33), tzompantli (plate 13), ball courts (plates 19, 27), and shrines (plate 29). The Titl and Ochpaniztli rituals show the two main forms of plan, with either tzompantli or banquet table, quauhxicalli and temple along the same axis.    (a) (b) Figure 2.9. (a) Tonalpohualli (divinatory calendar) panel with deities looking at stars (represented by half circle with small white dots) and Sun (represented with the other half as a solar disk), folio 11; (b) Deities within a temple in the New Fire ceremony, folio, 34, Codex Borbonicus (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0).  2.3.4 Codex Borgia  Description The Codex Borgia (26.5 x 27 cm, 14 strips folded to form 78 panels) is a ritual-calendrical pictorial manuscript from unknown origin, but its Mixteca-Puebla style and content are similar to codices from the Cholula-Tlaxcala area, the Tehuacán Valley and the Mixtec region (Jansen 2006). 33   Content  The content of the codex can be described in sections: • The sacred count of 260 days (tonalpohualli), their patron deities, and an alternative list of the 20-day signs with patron deities or divinatory signs, or both. • Predictions of climatic patterns in the different calendrical periods. • Rituals, centered around the magical passages from darkness to light, from death to life, and from sacrifice to the creation of fertility and power. • Complex scenes of trees, temples, deities and divinatory images associated with the four world directions and the center. • Deities that influence the travels of merchants and ambassadors (55), the life-giving force of Quetzalcoatl with the death god Mictlantecuhtli (56) and the patrons of marriages. • Depictions of the Sun god Tonatiuh, Mictlantecuhtli and Quetzalcoatl, Cihuateteo and Tonaleque, their associations with birds, and the numbers of day signs. The codex currently resides in the Biblioteca Apostolica Vaticana (Figure 2.10).  Summary of Architectural and Urban Depictions The architectural depictions include single temple pyramids (plates 33, 34, 35, 37, 45, 46, 49, 50, 51, 52, 55, 61, 62, 63, 64, 65, 66, 68, 74), tzompantli (plate 13), ball courts (plates 9, 21, 35, 40, 42), and shrines (plate 42). It is worth noting that plates 49 to 52 contain depictions of single pyramid temples in both front and side view.  34    (a) (b) Figure 2.10. (a) Tonalpohualli panel with deities playing on the Tlachtli (ball court), folio 21; (b) 20-day signs distributed over the bodies of four deities, surrounded by four great serpents, associated with the four directions, folio 72, Codex Borgia (Biblioteca Apostolica Vaticana, CC-BY-NC-SA 4.0).   2.3.5 Codex Boturini  Description The Codex Boturini (19.8 x 549 cm, 21 ½ panels) is a historical pictorial manuscript that chronicles the Mexica migration from 1168 to their arrival in the Valley of Mexico in 1355 (Glass and Robertson 1975:100).  Content  The codex follows a linear narrative that commences with the Mexica journey from Aztlan overseen by Huitzilopochtli, continues through their arrival in Chapultepec to the period of their subjugation to Colhuacan. (Glass and Robertson 1975:100). The codex currently resides in the Museo Nacional de Antropología in Mexico City (Figure 2.11).  35  Summary of Architectural and Urban Depictions The architectural depictions include single temple pyramids (plate 1), tzompantli (plate 10), and residences (plates 20, 21).   Figure 2.11. Departure from Aztlan, Codex Boturini (Museo Nacional de Antropología, CC-BY-NC-SA 4.0).  2.3.6 Codex Ixtlilxochitl  Description The Codex Ixtlilxochitl (31 x 24 cm, 11 leaves) is a historical manuscript that consists of three unrelated parts, two of which are pictorial (Glass and Robertson 1975:147). They may have been compiled by Fernando de Alva  Ixtlilxochitl, an early-seventeenth-century historian (Boone 2006).  Content  The first part (folios 94–104), dating from about 1600, is probably a partial copy of the Codex Magliabechiano. It includes an image and a description written in Spanish of the gods and ceremonies of 17 of the 18 months of the 365-day year, two drawings and texts of gods, and two drawings of funerary customs. The second part (folios 105–112) is comprised of six illustrations: four full-length portraits of Tetzcocan rulers, an illustration of the god Tlaloc and a depiction of the double temple pyramid in Tetzcoco (Glass and Robertson 1975:147-148). The third part (folios 113–122) is an explanation of the Aztec calendar written in Spanish (Boone 2006). The codex currently resides in the Bibliothèque Nationale de France (Figure 2.12). 36  Summary of Architectural and Urban Depictions The architectural depictions include a single temple pyramids (folios 99v) and the double temple pyramid of Tetzcoco which has subsequently been used by scholars to illustrate the Templo Mayor of Tenochtitlan.     (a) (b) (c) Figure 2.12. (a) Priest and sacrificed victim with temple in the background, folio 99v; (b) a representation of the god Tlaloc on top of platforms, possibly temalacatl, folio 110v; (c) Templo Mayor in Tetzcoco, folio 112v, Codex Ixtlilxochitl (Bibliothèque Nationale de France ,CC-BY-NC-SA 4.0).   2.3.7 Codex Magliabechiano  Description The Codex Magliabechiano (15.5 x 21.5 cm, 92 leaves) is a ritual-calendrical and ethnographic pictorial manuscript that consists of native drawings facing Spanish texts, developed for the Spaniards to record the calendars, festival ceremonies and customs of the Aztecs. It is believed that it is a copy created before 1566 of an older manuscript (Glass and Robertson 1975:155).  Content  The codex is divided in five sections: • A series of blankets with festival designs. 37  • The 20-day signs of the Aztec day-count. • The year signs in the 52-year cycle  • The eighteen monthly feasts. • Rituals and deities including funeral rites for people of different stations and occupations, and various forms of offerings and sacrifices. The codex currently resides in the Biblioteca Nazionale Centrale di Firenze (Figure 2.13).  Summary of Architectural and Urban Depictions The architectural depictions include single temple pyramids (40r, 70r, 79r, 87r, 91r), a ball court (80), and a temazcal (77r). The illustrations in this codex also demonstrate the transformation from the two-dimensional Aztec style to the three-dimensional European style that native painters started to incorporate in their paintings after colonization.    (a) (b) Figure 2.13. (a) Priest and sacrificed victim with temple in the background, folio 40r (b) a representation of the god Tlaloc on top of platforms, possibly temalacatl, folio 70r, Codex Magliabechiano, Nuttal facsimile (Biblioteca Nazionale Centrale di Firenze, CC-BY-NC-SA 4.0).   2.3.8 Codex Telleriano-Remensis  Description The Codex Telleriano-Remensis (32 x 22 cm, 50 leaves) is a ritual-calendrical and historical manuscript that was compiled from diverse local sources in the years following the conquest. It 38  is a hybrid document in which Indigenous artists painted the images while Spanish and Indigenous writers added annotations (Quiñones Keber 2006).  Content  The codex has three sections with different narrative styles. The first section (folios 385_01r to 385_07r) is an 18-month calendar with drawings of the gods of each period and a symbol for the nemontemi (the extra five days in the solar calendar). The second section (folios 385_08r to 385_24r) is a tonalpohualli (260-day divinatory almanac). The third section (folios 385_25r to 385_48r) is a pictorial annal for the period 1198-1562 in two major styles. The two final folios contain historical notices in Spanish with no images. The codex currently resides in the Bibliothèque Nationale de France (Figure 2.14).  Summary of Architectural and Urban Depictions The architectural depictions include single-temple pyramids (folios 385_29r, 385_38v, 385_41v, 385_42r ), a single temple pyramid with two entrances (folio 385_40r), double temple pyramids (385_36v, 385_39r, 385_40r), and a ball court (385_41r). In these depictions, the Templo Mayor is illustrated in two contexts, within a battle and in its dedication scene in 1487. It should also be noted that a single temple pyramid with two entrances is also illustrated as well as a side and front view of a single temple pyramid.  39    (a) (b) Figure 2.14. (a) Events related to famine suffered between 1504 and 1506 described in the context of a temple and sacrificial victim on frame assembled on platform, folio 41v; (b) battle between Mexico and Tlatelolco with double teocalli in the background, folio 26v, Codex Telleriano-Remensis, Loubat facsimile (Biblioteca Nazionale Centrale di Firenze, CC-BY-NC-SA 4.0).  2.3.9 Codex Xolotl  Description The Codex Xolotl (approximately 42 x 48 cm, 10 leaves forming a series of 8 maps) is a historical cartographic manuscript10 that details the history of the Tetzcocans from the initial migrations of the Chichimecs lead by Xolotl (1224) up to the "onset of the Tepanec war in                                                  10 Boone (2000a:183) describes de Codex as 10 leaves forming 8 maps; Douglas (19) as 6 leaves with 10 painted leaf and 3 fragments from one more painted leaf; and Glass and Robertson (241) as 6 leaves with 10 painted pages and fragments of a 7th leaf with 2 fragmentary pages based on the reproduction by Dibble in 1951. The painted sides of fragments 1A, 1B, and 1C were once attached to the backside of page 1, hence Dibble maintains that fragments 1A and 1B were part of the narrative of the Codex Xolotl. However, these fragments have noticeable compositional and stylistic differences.  40  1427"11 when Texcoco and Tenochtitlan rebelled against Azcapotzalco (Boone 2000a:183; Glass and Robertson 1975:241).   Content  The codex follows a narrative that can be divided into two sections. The first section (maps 1 to 6) contains extensive genealogical and political information that serves as a background for the second section (maps 7 to 10) which recounts the aggressions of the Tepanecs from Azcapotzalco against the Tetzcocans and its intended ruler, Nezahualcoyotl, that resulted in the Tepanec War of 1427 (Glass and Robertson 1975:241). The codex currently resides in the Bibliothèque Nationale de France (Figure 2.15).  Summary of Architectural and Urban Depictions The architectural depictions include single temple pyramids (maps 7 and 10), a ball court (map 9) and palaces (maps 8 and 9). Even though the Codex Xolotl focuses on Tetzcoco, it also serves as a map of the eastern region of the Valley of Mexico including Cholula across the mountains, Culhuacan and Chalco in the south, and Tenochtitlan across the lake (Boone 2000a:184).                                                   11 According to Thouvenot, the last date mentioned in the document is 1429 (67). 41   Figure 2.15. Map 9, Codex Xolotl (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0).   2.3.10 Historia Tolteca-Chichimeca   Description The Historia Tolteca-Chichimeca (30 x 22 cm, 52 leaves) is a historical and cartographic manuscript that chronicles the history of Cuauhtinchan from 1116 through 1544, although most of themes that dominate the manuscript, 49 of its 52 folios, focus on the pre-Hispanic period (Leibsohn 1993:12). It is one "of the major sources for the study of the early port-Toltec and subsequent history of the Chichimec migrations from Chicomoztoc to the Central Puebla region" (Glass and Robertson 1975:220).  42  Content  The Historia consists of three parts. The first two contain 22 leaves of the original and copies made by Aubin; modern editions combine the three parts, arrange the pages in logical sequence, and omit the Aubin copies. The narrative utilizes prose passages, songs, dialogues, glyphs and pictorial imagery to recount the migration of the Nonoalca and Toltec-Chichimec12 from Tula, the conquest of the Olmeca-Xicalanca at Cholula, the migration from Chicomoztoc, the founding of Cuauhtinchan, and the later history and regional battles of the inhabitants of Cuauhtinchan (Aguilar Moreno 2006:274). The Historia currently resides in the Bibliothèque Nationale de France  (Figure 2.16).  Summary of Architectural and Urban Depictions The architectural depictions include single temple pyramids (folios 07v, 19v, 26v, 27r, 38v, 39r), a round-temple pyramid (folio 41r), palaces (folios 08v, 14r, 24v, 25r, 27r, 32r, 42v, 43v, 43r), a ball court (folio 16v), and a complex assemblage (Cholula, folios 26v, 27r). The illustrations in the Historia Tolteca-Chichimeca also demonstrate the acculturation process suffered by native artists who continued using the two-dimensional Aztec style to draw representations of architecture that was changing. This is evident in the illustrations of temples where European-style churches with towers started replacing the blood-covered temples on top of the trapezoidal bases.                                                  12 The first encounter between the Toltec and the Chichimec is at a sacred cave known as Colhuacatepec, "Place of the Mountain of the Ancestors" (Leibsohn 1993:101). 43    (a) (b) Figure 2.16. (a) Migration scene in which two different temples are depicted, one in the traditional way (small mountain with stairs in the lower middle section), and the other with Spanish imagery (lower right), folio 7v; (b) players with ball in the characteristic I-shaped Tlachtli, folio 16v, Historia Tolteca Chichimeca (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0).  2.3.11 Mapa de Cuauhtinchan No. 2  Description The Mapa de Cuauhtinchan No. 2, also known as MC2 (109 x 204 cm, 1 map), is a historical and cartographic manuscript that chronicles the story of the migration of the people of Cuauhtinchan13. The "MC2 records events from the twelfth century, when the Chichimecs departed from Chicomoztoc, to the fifteenth century, when the Cuahtinchantlaca, pursued by the Tepeyacactlaca, fled across the Atoyac River with the Totomihuaque and Tecalca (Yoneda 2007:162-163). The manuscript also contains information about geography, religious rites, political activities, boundaries and chronology.                                                  13 The MC2 and the Historia Tolteca-Chichimeca are the only Cuauhtinchan documents that narrate the emergence from Chicomoztoc and subsequent journey to Cholula before arriving in Cuauhtinchan (Boone 2000a:182). 44   Content  The MC2 is part of a group of six cartographic histories from the Altepetl of Cuauhtinchan located southeast of the ancient city of Cholula. The narrative tells the story from their point of origin, the mythical cave, their journey through Cholula-an important civic and religious centre- to the vicinity of the Amozoc Tepeaca range (Boone 2000a:173). The left side of the MC2 concerns the events related to their departure and arrival to Cholula; the right side emphasizes socio-political events. The purpose of the MC2 was to prove the historical priority of Cuauhtinchan over Tepeaca (Yoneda 2007:165-166). The MC2 currently resides in the private collection of the late Angeles Espinosa Yglesias (Figure 2.17).  Summary of Architectural and Urban Depictions Besides containing numerous toponymic glyphs, the MC2 has several architectural depictions including single temple pyramids, round temple pyramids, a round temple on a cliff, palaces, ball courts and a complex assemblage (Cholula). Furthermore the MC2 is one of the most outstanding visual representations of the sacred landscape comprised of mountains, rivers, and both natural and modified caves (Yoneda 2007:167).   Figure 2.17. Mapa de Cuauhtinchan No. 2 (Carrasco and Sessions 2007:Figure 1). 45   2.3.12 Mapa Quinatzin  Description The Mapa Quinatzin (77 x 44 cm, 2 sewn leaves; 34.5 x 43.5 cm, 1 separate leaf) is a historical manuscript that depicts events in the time of Quinatzin and Techotlalatzin as well as the palace of Nezahualcoyotl in Texcoco in the late 15th century (Mohar Betancourt 110).  Content  The first sewn leaves of the manuscript illustrate events that happened in the time of Quinatzin and Techotlalatzin. The separate leaf shows the palace of Nezahualcoyotl, the various sections in which it was divided, and the towns subject to Texcoco and their rulers (Glass and Robertson 160). The codex currently resides in the Bibliothèque Nationale de France (Figure 2.18).  Summary of Architectural and Urban Depictions Even though the first leaf contains several toponyms, the only architectural depiction of the palace of Nezahualcoyotl.   Figure 2.18. Depiction of Palace (Tetzcoco), Mapa Quinatzin (Enhanced copy, original Bibliothèque Nationale de France CC-BY-NC-SA 4.0),  46  2.3.13 Summary of Architectural and Urban Depictions in Pictorial Manuscripts  The analyses of the codices revealed that the most common types of architectural depictions in pictorial manuscripts are single temple teocallis, nobility dwellings, double temple teocallis, tlachtlis (ball courts), tzompantlis (skull racks) and circular base teocallis (Table 2.1). Single temple teocallis are consistently utilized throughout manuscripts as phonetically and semantically defined logograms to represent toponyms and personal names, and are often combined with other glyphs (Yoneda 2007:166).   Double temple teocallis appear only in reference to Tenochtitlan-Tlatelolco and Texcoco, the main city-states of the Triple Alliance, which dominated the Aztec empire from 1428 until the defeat by the Conquistadores in 1521. The representation of the double temple teocalli of Texcoco in the Codex Ixtlilxochitl provides unique architectural details of this structure: an ample base with priests precincts on both sides, four stepped platforms in the form of truncated pyramids, and two temples on top, one dedicated to Tlaloc (north) and the other to Huitzilopochtli (south). Even though the representations of the double teocalli of Tenochtitlan—the Great Temple of the Aztecs—in the Codex Azcatitlan are not architecturally accurate, they demonstrate the process of acculturation suffered by Aztec scribes after the Conquest. During this time, the traditional two-dimensional drawings began changing to three-dimensional representations of stories, people and architecture.  47  Table 2.1. Summary of the type of architectural and urban depictions in Pictorial Manuscripts.  Type of Architectural Structures Codex Aubin Codex Azcatitlan Codex Borbonicus Codex Borgia Codex Boturini Codex Ixtlilxochitl Codex Magliabechiano Codex Telleriano-Remensis Codex Xolotl Historia Tolteca-Chichimeca  Mapa de Cuauhtinchan No. 2 Mapa Quinatzin Single Temple Teocalli 4 4 2 19 1 2 5 4 2 6 5   Double Temple Teocalli 1 7       1   4         Circular Base Teocalli   1               1 3   Carved Teocalli                         Tzompantli 1 2 1 1 1               Tlachtli     2 2     1 1 1 1 4   Rectangular Base Shrine     1 1                 Circular Base Shrine                         Priests Precinct                     2   Warriors Precinct                         Nobility Dwellings                 2 9 10 1 Commoner Dwellings         3               Calmecac                         Momoztli at centre of courtyard                         Perimetral wall                         Rectangular Platform                         Telpochcalli                         Temazcalli                         Quauhxicalli                         Temalacatl                         Temazcal 2           1           Pools                         Gardens                         Complex Assemblage 1   1             1 1    After the single temple teocalli, the tlachtlis (ball court) and the tzompantlis, although not numerous, appear in most codices. In contrast, nobility dwellings, though abundant in the Historia Tolteca-Chichimeca and the Mapa de Cuauhtinchan No. 2, are not present in most manuscripts, the only clear exception being the Mapa Quinatzin (Table 2.2).  48  The circular base teocallis can easily be distinguished by their conical thatched roofs. The different views (front, side, isometric) of these teocallis included in the Mapa de Cuauhtinchan No. 2 (MC2) reveal their unique architectural characteristics, particularly the cylindrical shape of the temple on top of their truncated conical stepped platforms. The MC2 also contains a circular base teocalli on the slope of a mountain, which might indicate their importance within the sacred landscape.  Table 2.2. Frequency of the type of architectural depictions in Pictorial Manuscripts.    In addition to architectural structures, there are also complex assemblages depicted in pictorial codices, mainly the ceremonial centres of Cholula and Tenochtitlan, as well as the ritual space in 49  the Codex Borbonicus. These assemblages reveal the two main forms of plan common in Central Mexico, with either tzompantli or banquet table, quauhxicalli and temple along the same axis.  2.4 Pictorial Administrative Manuscripts  When Hernán Cortes arrived in 1519 AD, the Aztec Empire had expanded from the Valley of Mexico to a vast area of Central Mexico in a system of tributary provinces and strategic provinces that extended from the Pacific Ocean to the Atlantic Ocean and as far south as Guatemala (Berdan et al. 1996:5). The tributary provinces had the obligation of sending regular payments of goods and services, however, the goods and services sent by the strategic provinces were defined as gifts rather than tribute obligations, thus making it a less oppressive relation (Evans 2004:470). These imperial relations resulted in a complex system of recordkeeping of various classes and at different territorial levels. Several imperial and local level records survived both in pictorial and written manuscripts. Imperial records such as the second section of the Codex Mendoza, have detailed lists of goods from the tributary provinces. Local level records, such as the pictorial codices from Tepetlaoztoc, have household censuses and household land cadasters (Williams and Jorge 2001:186).  Even though some land records had existed since the 19th century, they had barely been studied due to the lack of understanding of their mathematical conventions. It was not until 1980 that Harvey and Williams decoded the numerical portions of the Códice de Santa María Asunción. Williams and Jorge continued this research and later found geometric algorithms for surface area computation that may have been employed by Acolhua-Aztec surveyors (2001:185).  Another type of pictorial manuscript included colonial period administrative documents that were produced within the Spanish legal system. The information contained in these manuscripts gave a wealth of detailed local information before the Conquest and during the early Colonial period (Smith Aztec 2008:18). These documents comprise maps as well as legal processes.  In spite of the fact that collections such as the Mapas, Planos e Ilustraciones from the Archivo General de la Nación has more than 8000 documents in its archives or that other pictorial-50  administrative documents haven been in foreign collections for centuries, some scholars have managed to study them. These studies have mostly focused on their economic and legal content or on their mathematical representations. However, they have not been analyzed from an architectural-urban point of view. Hence, a representative sample of these manuscripts was selected for analysis. A summary of these meticulous analyses is included in this section. Unlike the pictorial manuscripts that contain representations of Mesoamerican building types, the pictorial-administrative manuscripts demonstrate the utilization of precise geometric and mathematical system that allowed the Aztecs to divide property or settle legal disputes. These analyses provided the confirmation that this knowledge was applied when they planned their cities and constructed their buildings.  2.4.1 Codex Mendoza  Description The Codex Mendoza (32.7 x 22.9 cm, 72 leaves) is a historical, economic and ethnographic manuscript that recounts history of the Mexica from 1325 to 1518,14 their tributes to the Aztec empire and Aztec life through images and descriptions written in Spanish for sentences and Nahuatl for names. It is believed to have been commissioned by the first viceroy of New Spain, Don Antonio de Mendoza, for presentation to Charles V (Glass and Robertson 1975:160).   Content  The codex has three distinct sections. The first section (folios 2r-16v) documents the founding of Tenochtitlan and records the history of the conquests of the Mexica by individual ruler. The second section (folios 17v-55r) is a detailed account of the tribute obligations of 371 city-states grouped in 38 provinces. The third section (folios 56v-71r) provides a pictographic account of the daily existence of the Mexica as well a drawing of the royal palace of Motecuhzoma. The° first two sections appear to have been copied from extant pre-Hispanic documents, but the final section was created at the request of the Spanish (Berdan and Anawalt 1997:xii). The codex currently resides the Bodleian Library at Oxford (Figure 2.19).                                                  14 Glass and Robertson date it from 1325 through 1521 (1975:160), but this date is disputed among scholars who believe that three years were added at a later time. 51   Summary of Architectural and Urban Depictions The significance of the Codex Mendoza in architectural research is twofold; it not only contains urban and architectural depictions, but also mathematical knowledge that can be deduced from the tribute owed by each province.  The architectural depictions include single temple pyramids (folios 2r, 2v, 3v, 4v, 5v, 6r, 7v, 8r, 10r, 10v, 12r, 13r, 13v, 15v, 16r, 16v, 19r, 20v, 23r, 24v, 27r, 32r, 33r, 37r, 38r, 39r, 40r, 42r, 44r, 46r, 48r, 49r, 51r, 52r, 63r, 64r, 67r), a double temple pyramid (folio 10r), tzompantlis (folios 2r, 35r), ball courts (folios 8r, 16r, 31r, 36r, 45r), calmecac (folio 61r), and the palace of Motecuhzoma(69r).  Nonetheless, it should be noted that the majority of these architectural depictions are the toponyms of the city-states that were under the political domination of the Aztec empire. These cities are represented with a temple glyph complemented by a place glyph. In the first section of the codex, the temples are on fire, as this signifies that they were conquered. The second section has simplified versions of toponyms, but few of them use a temple in their name. The third section has only three temples shown in the context of an activity.  52    (a) (b) Figure 2.19. (a) Foundation of Tenochtitlan, folio 2r; (b) tribute list with number of items in Aztec units, folio 24r, Codex Mendoza (Bodleian Library, CC-BY-NC-SA 4.0).  2.4.2 Codex of the Marquesado del Valle  Description The Codex of the Marquesado del Valle (28 single large-format leaves with paintings and text in Nahuatl written in Latin characters and two booklets totaling 102 leaves) is a pictorial legal manuscript that contains 28 separate petitions from different leaders and towns of the Marquesado del Valle protesting seizures of lands and sugar mills by Hernán Cortés.  Content This codex records ownership of land parcels, place names and parcel size. It also specifies the type of production and quantities and gives the names of ruling chiefs and other miscellaneous 53  information. The codex currently resides in the Archivo General de la Nación de México (Figure 2.20.)  Summary of Architectural and Urban Depictions The significance of the Codex of the Marquesado del Valle is that it clearly illustrates parcel dimensions following mathematical conventions.    (a) (b) Figure 2.20. (a) and (b) Perimeter dimensions of property in Aztec units and tribute owned, Codex of the Marquesado Del Valle (Archivo General de la Nación de México, CC-BY-NC-SA 4.0).  2.4.3 Plan and Title of a Property in Tenochtitlan  Description  The Plan and Title of a Property in Tenochtitlan is a pictorial legal manuscript that depicts the legalization of a genealogy (Caracas).  Content The codex records family members, ownership of possessions and the plan of the property. The manuscript currently resides in the Bibliothèque Nationale de France (Figure 2.21). 54  Summary of Architectural and Urban Depictions The significance of the Plan and Title of a Property in Tenochtitlan is that it clearly illustrates the use of two types of units, one to describe quantities (blue glyphs on top) and another to record the measurements of the property (hands, dots and arrows along the perimeter of the walls).    Figure 2.21. Plan and Title of a Property in Tenochtitlan (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0).  2.4.4 Codex Vergara  Description The Codex Vergara (31x22 cm, 55 leaves) is an economic (census and cadastral) manuscript that contains a pictorial census and two cadasters for each of the five named localities in the Tepetlaoztoc region. It is probably dated around 1539 (Glass and Robertson 1975:229).  55  Content The codex has three sections of recorded information. The first section includes the demographic composition of each household; the second section has cadastral drawings of the land parcels; and the last section includes another cadastral register in a different format of the same landholdings. The codex currently resides in the Bibliothèque Nationale de France (Figure 2.22).  Summary of Architectural and Urban Depictions The significance of the Codex Vergara is that it is one of the clearest demonstrations of the use of linear measurements in the context of properties with different geometric configurations.    (a) (b) Figure 2.22. (a) Demographic composition of each household; (b) drawings of parcels with area and perimeter measurements in Aztec units (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0).  56  2.4.5 Codex Santa María Asunción  Description The Codex Santa María Asunción (31x21 cm, 80 leaves) is an economic (census and cadastral) manuscript that contains pictorial registers of person and properties for a number of named localities in the Tepetlaoztoc region of the eastern valley of Mexico. The dates mentioned in the Nahuatl texts are 1550, 1571 and 1579 (Glass and Robertson 1975:88).  Content Similar to the Codex Vergara, this codex has three distinct registers of information: a census by household (tlacatlacuiloli); a description of each household's landholdings, which includes perimeter measurement, general shape and soil type (milcocoli); a second register of the same lands which records the quantity of land in each parcel depicted (tlahuelmantli) (Harvey 1986:275). The codex currently resides in the Biblioteca Nacional de México.  Summary of Architectural and Urban Depictions Similar to the Codex Vergara, the significance of the Codex Santa María Asunción is that it is one of the clearest demonstrations of the use of linear measurements in the context of properties with different geometric configurations.  2.4.6 Oztoticpac Lands Map  Description The Oztoticpac Lands Map (76 x 84 cm) is a litigation map of Oztoticpac, an estate in Texcoco,  related to a lawsuit concerning the estate of Don Carlos Ometochtli Chichimecatecotl. It is dated approximately 1540.  Content The map contains detailed drawings of several houses and over 75 land parcels, including shapes and measurements, of properties once owned by Don Carlos. The map currently resides in the Library of Congress Geography and Map Division Washington, D.C. (Figure 2.23). 57  Summary of Architectural and Urban Depictions The Oztoticpac Lands Map is the clearest demonstration of the use of linear measurements in the context of properties with different geometric configurations in a small scale and larger properties in an urban scale.   Figure 2.23. Plan of palace and surrounding land in Aztec units (upper left corner) and land parcels shape and dimensions in Aztec units (right half of image), Oztoticpac Lands Map (Library of Congress Geography and Map Division Washington, D.C., CC-BY-NC-SA 4.0).   58  2.4.7 Summary of Architectural and Urban Depictions in Pictorial-Administrative Manuscripts  The relevance of these pictorial administrative manuscripts rests on the fact that they reveal the clear mathematical and geometrical systems the Aztecs utilized for recordkeeping and land surveying. The Codex Mendoza is a clear visual representation of the base-20 mathematical system utilized by the Aztecs. On the other hand, the Codex of the Marquesado del Valle, the Codex Vergara, the Codex Santa María Asunción and the Oztoticpac Lands Map provide not only a wealth of administrative information including household composition, soil type and crops, but also land survey data comprising shape, perimeter and area of plots.  The information contained in these documents suggests a conceptualization of area attributes of geometric forms such as rectangles and triangles, as well as calculations of land areas. These calculations required utilizing several algorithms requiring the functional equivalents of addition, subtraction, multiplication and division (Williams and Jorge 2001:187), knowledge that was applied to urban planning and architecture by extension. Scholars such as Rivera (1997) and Clark (2010) have argued that this system of linear measurements was employed in the design of the ceremonial precinct of Tenochtitlan.  2.5 Eyewitness Accounts by the Conquistadores  There are a limited number of eyewitness accounts by Spanish participants in the Conquest including those of Hernán Cortes, Bernal Diaz del Castillo, Francisco de Aguilar, Andrés de Tapia and the "Anonymous Conqueror." These are supplemented by several smaller claims and legal testimonies, as well as other stories, written by people that did not accompany Cortés, such as Pedro Martir de Angleria and Francisco López de Gómara, who utilized the returning conquistadores as the sources of their accounts (Hassig 2006:3). They were initially motivated by their desire to narrate the events in which they participated, but their motivations soon changed to suit their interests and to claim from the Spanish crown more slaves, properties or administrative positions to reward their exploits (Martínez 1989:679).  59   Even though the eyewitness accounts have been studied as a documentary or literary genre, they have only been utilized to illustrate the grandeur of Tenochtitlan in the context of other studies in spite of their detailed architectural and urban descriptions. However, two sources, the Cartas de Relación (Letters from Mexico) by Hernán Cortes and the Historia Verdadera de la Conquista de la Nueva España (The True History of the Conquest of New Spain) by Bernal Díaz del Castillo contain ample descriptions architectural and urban design of the city and its landscape surrounded by water and mountains. These descriptions are valuable because they saw Tenochtitlan and its ceremonial precinct relatively intact before the destruction that followed. Their accounts include descriptions of the ceremonial precinct, its size and the number of temples, as well as the layout of the Templo Mayor and the Quetzalcoatl temple. These simplified descriptions are not intended to be precise or provide a complete view of the complex layout of the ceremonial precinct, as Cortés and Díaz del Castillo selected different structures and omitted others. (Cortés does not include the ball court, for example.) Nonetheless, they complement other historical sources and archaeological evidence and transmit the grand design of the buildings, the city and its landscape.  2.5.1 Hernán Cortes  2.5.1.1 Description The Cartas de Relación is a compilation of the five letters that Hernán Cortes wrote between 1519 and 1526 to Emperor Charles V of Spain. They narrate the main events of his exploits from his landing on the Mexican coast and the conquest of Tenochtitlan, to his failed expedition to Honduras (Martínez 1989:681).  2.5.1.2 Summary of Architectural and Urban Depictions In the Second Letter, signed on October 30, 1520, Cortés narrates the wars and the alliances he made on his journey toward the Valley of Mexico. His account culminates in his impressive description of Tenochtitlan, the ceremonial precinct including the Templo Mayor, and the palace Motecuhzoma. Even though he is disgusted with the practice of human sacrifice, he conveys great admiration for the high degree of civilization he has witnessed, "to the point of frequently 60  comparing Aztec achievements with those of Arab and Christian civilizations" (Delgado 2006). When the Second Letter was first published in Seville in November 1522, this edition contained no map. Nonetheless, when it was translated into Latin and published in Nuremberg in 1524, it was accompanied by a woodcut map of Tenochtitlan. This map shows Tenochtitlan in the centre of an azure lake (in the hand-coloured versions) connected by causeways and surrounded by neighboring cities around the lake (Figure 2.24). This was the first image that Europe had of the city and eventually became the most widespread (Mundy 1998:11). Even though the map was carved by a European, it reveals many details that are not described in the Second Letter of Cortés, which leads Mundy to believe that it was based in an Indigenous map (1998:27). Together, the descriptions of Cortés and the Nuremberg map contain important urban, architectural and astronomic information including: the layout of Tenochtitlan, the design of the ceremonial precinct and its buildings, the connection to the landscape via its main urban axes and the rising Sun represented as a face rising between the double temples of the Huey Teocalli (Great Temple).   Figure 2.24. Map of Tenochtitlan from the Latin translation published in Nuremberg in 1524. The map is rotated 90° clockwise while the ceremonial precinct is rotated 90° counterclockwise (Newberry Library, Chicago, CC-BY-NC-SA 4.0).  61  2.5.2 Bernal Díaz del Castillo  2.5.2.1 Description The Historia Verdadera de la Conquista de la Nueva España (Figure 2.25) is an account that not only chronicles the Spanish conquest from 1517 to 1521, but also the public affairs in New Spain through 1568. It is believed that Bernal Díaz del Castillo utilized as sources for his work the published letters of Cortés (1522–1526), the History of the Conquest of Francisco López de Gómara (1552) and even Mexican pictorial manuscripts (Adorno 2006).  2.5.2.2 Summary of Architectural and Urban Depictions Similar to Cortés, the significance of the vivid descriptions of Díaz highlight the architectural and urban characteristics of the city and its surrounding landscape:  And when we saw all those cities and villages built in the water, and other great towns on dry land, and that straight and level causeway leading to Mexico [i.e. Tenochtitlan], we were astounded. These great towns and cues [i.e., temples] and buildings rising from the water, all made of stone, seemed like an enchanted vision from the tale of Amadis. Indeed, some of our soldiers asked whether it was not all a dream. It is not surprising therefore that I should write in this vein. It was all so wonderful that I do not know how to describe this first glimpse of things never heard of, seen or dreamed of before…  And when we entered the city of Iztapalapa, the sight of the palaces in which they lodged us! They were very spacious and well built, of magnificent stone, cedar wood, and the wood of other sweet-smelling trees, with great rooms and courts, which were a wonderful sight, and all covered with awnings of woven cotton (Diaz 2004:269). 62    Figure 2.25. Historia Verdadera de la Conquista de la Nueva España (University of British Columbia-Rare Books and Special Collections).  2.6 Chronicles Compiled by the Missionaries  Following the military conquest, the Catholic Church commenced the religious conquest and sent a group of missionaries in 1524. Far from the influence of church and civil authorities in Spain, they began to use unconventional approaches for the conversion of the natives such as building open chapels, organizing theatrical performances and utilizing their pictorial manuscript tradition to convey their message. A few of these friars "sought to document their role in the progress of evangelization as well as to preserve elements of indigenous culture" (V. Smith 1997:213). Some of them collected and recorded information from Aztec informants with the purpose of understanding their religion in order to aid their conversion to Christianity. Among these friars were Andrés de Olmos, Toribio de Benavente Motolinía, Bernardino de Sahagún, Juan de Torquemada and Diego Durán. In some cases, such as Sahagún and Durán, they had 63  images copied from native manuscripts for their own compilations, a practice that Felipe II outlawed in 1577 (García Ayluardo 1997:247).   The compilations by Fray Bernardino de Sahagún and Fray Diego Durán are considered one of the most valuable sources of information about the native culture in Central Mexico due to the wealth of information contained in them. However, in spite of the fact that they have been thoroughly analyzed and referenced by multiple scholars in several disciplines, their urban and architectural depictions have not been analyzed.  2.6.1 Fray Bernardino de Sahagún  2.6.1.1 Description Fray Bernardino de Sahagún (1499-1590) arrived in Mexico in 1529 with a second group of Spanish missionaries at a turbulent time in the new colony. By 1536 he was appointed to teach Latin in the Colegio Imperial de la Santa Cruz Tlatelolco, a special school for the sons of the native nobility, some of whom eventually became his assistants. Even though he collected and compiled material during those years, it was not until 1558, when he was formally commissioned to write "all that he considered useful for the conversion of the natives," that he devoted himself to the investigation of Aztec religion, customs and natural history. He recruited informants and artists, worked with pictorial manuscripts, talked to elders, diviners, herbalists and merchants, and even prepared questionnaires to gather and record information (D'Owler and Cline 1975:186).   This material was eventually compiled and translated into a comprehensive encyclopedia of Aztec culture: the Historia General de las Cosas de la Nueva España, known as the Florentine Codex15 (Anderson 1982:3), which is considered to be one of the most valuable primary sources for the study of Aztec culture at the time of European contact; it is a comprehensive and                                                  15 The name Florentine Codex was adopted as the standard appellation for the edition of Anderson and Dibble of the General History of the Things of New Spain because Edgar L. Hewett, the founder and first director of the School of American Archaeology, so designated it. More formally, Hewett referred to it as "the Great Florentine Codex." It has also other labels. Officially it is the manuscript of the Biblioteca Medicea-Lorenziana Palat in Florence (Anderson 1983:3). 64  methodical firsthand account of the indigenous peoples of Central Mexico (Nicholson 2000:21). The Sahaguntine oeuvre encompasses detailed descriptions in Nahuatl and in Spanish of the Aztec Gods, their religious beliefs and rituals, and the theology involved in the indigenous cosmology. It also offers a depiction of the Aztec people themselves, including their history, philosophy, society, politics, economics and medicinal practices and the natural history of New Spain. In the words of H.B. Nicholson, "it is the most remarkable account of a non-Western culture ever composed and a primary source about the Aztecs for modern-day scholars" (2000:34).  The interest of Sahagún in native culture caused his work to be scrutinized by the Inquisition in 1575. His writings were confiscated, and they were not found again until the eighteenth century. Nonetheless, a number of manuscripts representing successive stages in the compiling of the Historia survive. They are in Nahuatl, Spanish or both; some are illustrated. The Nahuatl texts and the drawings are considered the work of the native informants of Sahagún (Glass and Robertson 1975:187).  The main manuscripts are the Codices Matritenses and the Florentine Codex. The Codices Matritenses contain various early manuscripts of the Historia, but only two are illustrated: the Primeros Memoriales and the Manuscrito de Tlatelolco. Conversely, the Florentine Codex, his final compilation with parallel texts in Nahuatl and Spanish, is profusely illustrated (Glass and Robertson 1975:188).  2.6.1.2 Summary of Architectural and Urban Depictions The Primeros Memoriales contains multiple architectural depictions of single temples, double temples, ball courts, skull racks, residential structures, and shrines. Most of these architectural depictions are inscribed in frames with descriptions of the festivities that took place during the 18 months of the Xiuhpohualli (solar) year. Hence, they place in urban context the locations of buildings, as different rituals were performed in each one of them following a certain order (Figure 2.26).  65   Figure 2.26. Quauitleoa (top); Tlacaxipehualiztli festival within an architectural arrangement that includes two temples, a central platform, and a tzompantli or skull rack (middle); and Tozoztontli festival (bottom), folio 250r, Primeros Memoriales (Real Biblioteca de Madrid, CC-BY-NC-SA 4.0).  It is believed that the architectural depiction of the ceremonial precinct is the most complete plan remaining of the centre of Tenochtitlan, because it contains the main elements of Aztec architecture: the main double teocalli, the tzompantli (skull rack), the tlachtli (ball court), the circular-base teocalli and other single temple teocallis; and the main elements of urban planning: an axial plaza plan with the main double teocalli at the intersection of its axes (Figure 2.27).  66   Figure 2.27. Depiction of the ceremonial precinct, Primeros Memoriales, folio 268ra (Real Biblioteca de Madrid, CC-BY-NC-SA 4.0).  Furthermore, the 12 volumes of the Florentine Codex are also extensively illustrated with 1 846 drawings, but it is Book 2-The Ceremonies where most architectural depictions are included in the detailed narrative of the Xiuhpohualli feasts. Nonetheless, this book includes an appendix where there is "a true [relation] of all [the temples] which were the temples of the Mexicans" comprised of 78 structures, but it does not include a map as it was apparently removed at some point (Anderson and Dibble 1982:15-21).  The written descriptions contained in the Appendix of Book 2-The Ceremonies reveal a standard arrangement of elements (temple, bathing place, calmecac, skull rack and ball court) that repeats in each temple grouping. The description of the ceremonies, along with the list of the temples, uncover an intricate system of relationships between the rites and architecture which were possibly reflected as a complex arrangement of temple groupings within the ceremonial precinct rather than the axial and almost symmetric arrangement depicted in the Primeros Memoriales plan. Hence, the oeuvre of Sahagún provides an extensive visual and written resource for the study of Aztec architecture and urban planning. 67  2.6.2 Fray Diego Durán  2.6.2.1 Description Fray Diego Durán (1537-1588) arrived in New Spain as a child where he soon learned Nahuatl. He entered the Dominican order in 1556 and was later commissioned to study the religion and the ceremonies in Mexico for the purpose of evangelization. The result of this commission was one volume comprising The Book of the Gods and Rites (1574–1576) and The Ancient Calendar (1579), and a second volume titled The History of the Indies of New Spain (1581) (Heyden 1994).  2.6.2.2 Summary of Architectural and Urban Depictions Durán included some meticulous descriptions of architecture in his works. In The Book of the Gods and Rites, he described the rituals performed in the temple groupings within the ceremonial precinct, but supplemented these descriptions with few illustrations. In The History of the Indies of New Spain he gave an account of the foundation of Mexico-Tenochtitlan and the construction of the temple dedicated to Huitzilopochtli.  The chapters of The Book of the Gods and Rites are organized according to gods, rituals or temples, hence it is possible to extract from each chapter the architectural descriptions and their locations as not all the festivals take place in Tenochtitlan.  Even though the descriptions of Durán are romanticized versions of the architecture that had already been destroyed, they are valuable for the study of Aztec architecture because they illustrate the type, quantity and relationships among buildings. Furthermore, his descriptions reveal that there were several temple complexes within the ceremonial precinct, the presence of other buildings in other places outside of Tenochtitlan, and the importance of the surrounding landscape, such as mountains are always an integral part of the illustration (Figure 2.28).  68    (a) (b) Figure 2.28. (a) Double Teocalli dedicated to Tlaloc and Huitzilopochtli, Cerro Tlaloc and Cerro Telapon frame the twin temples, folio 131r; (b) victim on Temalacatl platform fighting warrior, Historia de las Indias de Nueva España e islas de la Tierra Firme by Diego Durán (Biblioteca Nacional de España, CC-BY-NC-SA 4.0).  2.7 Archaeological Evidence   The body of archaeological research about Aztec sites is quite limited compared to other sites in Mesoamerica. Smith and Berdan have interpreted this invisibility as a lack of understanding of the Aztec empire due to several reasons. According to them, some scholars do not agree that the Aztec was a "real" empire, thus they do not acknowledge the existence of Aztec archaeological remains outside the Valley of Mexico. A second reason is that, even though the Aztec polity might be considered an empire, its organization in tributary and strategic provinces did not require major investments in construction. The third reason is that archaeologists have not performed enough problem-oriented fieldwork projects to evaluate the effects of Aztec imperial strategies in other provinces (Smith and Berdan 1992:353). However, their interpretation suggests a primitivist approach that ignores the socio-political context of archaeological research 69  and its role in the construction of state-sponsored national identities (Errington 1998: 161), which actually began with the Aztec themselves.   Scholars agree that the Aztecs constructed their identity by assimilating the cultural traits of people who had preceded them and deliberately setting out to perpetuate a tradition derived from the Toltecs with whom they wanted to be identified (Molina 1987:104). They incorporated Toltec myths, some forms of social, politic and economic organization, as well as rituals and ceremonies with their own. In the case of architecture and urban planning, there is enough archaeological evidence of the integration of these characteristics in their architectural manifestations (Matos 1981:259). When the Aztecs arrived to the Valley of Mexico around 1250 AD, they had no power and no land, but by 1430 they had begun their military expansion. The resulting wealth and power enabled them to start the expansion of the island city.   Furthermore, the interpretation of Smith and Berdan (1992) does not take into account the extensive research carried out by scholars in Mexico who have constructed a "succession of powerful secular images and texts that have moulded the consciousness of the past, and beliefs in destiny, that are closely identified with distinct political regimes" (Shelton 1995:69). Even though a large part of archaeological research has focused on sites with monumental architecture such as Teotihuacan and Tenochtitlan, other Aztec city states have also undergone archaeological fieldwork. However, access to this research has been limited as it has been barely published. This has produced a dissimilar body of knowledge, as the quality and quantity of available information for Aztec sites varies from scattered reports of smaller sites to a considerable number of studies about the ceremonial precinct of Tenochtitlan, particularly the Huey Teocalli (Templo Mayor) of Tenochtitlan.  Apart from this unbalanced research corpus, the biggest challenge is the location of archaeological remains  and the amount of excavations done on these sites. Some sites lie within—or under—larger colonial cities such as Tenochtitlan, Tlatelolco and Tenayuca; some within smaller colonial cities such as Santa Cecilia, Tenayuca, and Teopanzolco (Figure 2.29); others scattered among small villages and farmland such as Calixtlahuaca and Huexotla; while 70  still others on areas than have been barely excavated, such as Quauhtochco, or not excavated at all, such as Cuentepec.  An additional challenge is the level of conservation of architectural structures. Even though some can be identified by their architectural characteristics, like the double temple teocalli, the circular base teocalli and the tlachtli (ball court), others such as a rectangular base shrine could be considered as a platform or a small single temple teocalli. Larger structures with several rooms can also be interpreted as palaces, nobility dwellings, or calmecacs (schools) unless they can be identified through ethno-historical sources such as the calmecac of Tenochtitlan.  Despite these challenges, single temple teocallis, rectangular base shrines, nobility dwellings, circular base teocallis and circular base shrines are the most common architectural structures in Aztec archaeological sites. However, the most distinctive Aztec architectural structure, the double temple teocalli, is only present in five sites: Tenochtitlan, Tlatelolco, Tenayuca, Santa Cecilia Acatitlan and Teopanzolco. Consequently, the study of the Aztec architecture and urban planning is a complex endeavour, as it involves searching for published and unpublished information in several types of media such as archaeological reports, books, articles in scholarly and popular literature, image databases and recorded material on video. Since most sites are located in urban areas, digital applications such as Google Maps, Google Earth and custom geometric applications are needed to analyze sites in the context of the existing city, as scholars such as Tichy (1976) and Šprajc (2001) have demonstrated that churches and their surrounding areas follow the same orientation as the Aztec site located there before the Conquest.  71   Figure 2.29. Map of Valley of Mexico in 1519 (Pasztory 1983: Figure 1).  72  2.8 Monumental Sculpture  Since the discovery of the Aztec Sun Stone, the Coatlicue and the Stone of Tizoc and the subsequent publication of A Historical and Chronological Description of Two Stones which were found in 1790 in the Principal Square of Mexico During the Current Paving Project by Antonio León y Gama in 1792, most studies have concentrated on interpreting their religious, political, and artistic imagery, mainly of the Sun Stone.16 Albeit some of these studies marveled at the geometry of these monumental sculptures, only Alfonso Caso measured the Sun Stone so that its geometric properties could be analyzed. A mathematical analysis of several sculptures was done by Raúl Noriega in 1953, but it was not until 1978 that architect Carlos Chanfón Olmos attempted a geometrical analysis of the Sun Stone. Ramírez Bautista continued this work in 1995 by painstakingly measuring the Sun Stone, the Stone of Tizoc and the Ex-archbishopric's Palace Stone and analyzing their regulating lines. He demonstrated that a series of geometrical principles were embedded in the design of these monumental sculptures (Ramírez 1995).   Furthermore, in 1996 Rivera applied a geometrical analysis approach on Aztec architecture on the digital interpretation of the ceremonial precinct of Tenochtitlan, where archaeoastronomical and geometrical principles were utilized for reconstructing the ceremonial precinct of Tenochtitlan. Martinez del Sobral furthered explored geometrical principles on several examples of Mesoamerican art, sculpture and architecture in 2000.  Aztec monumental sculpture should be considered as a source for understanding Aztec architecture as it contains the underlying mathematical and geometrical principles that must have been applied to architecture (Figure 2.30). Furthermore, the only existing piece of monumental sculpture in the form of a temple, the Teocalli de la Guerra Sagrada (Teocalli of the Sacred War or the Temple Stone), displays a solar geometric design in its centre which confirms the direct relationship between the rising and the setting of the Sun in the context of carved Tlaloc and Huitzilopochtli figures on each side representing Cerro Tlaloc and Cerro Telapon.                                                   16 A selection of the multiple studies that refer to the Aztec Sun Stone can be found in The Aztec Calendar Stone by Khristaan Villela and Mary Ellen Miller.  73  (a) (b) (c) Figure 2.30. (a) The Aztec Sun Stone, (b) the ex-Archbishopric's Stone, (c) the Teocalli (Museo Nacional de Antropología, Mexico CC BY-NC-SA 4.0).  74  2.9 Urban and Architectural Models  In the historiography of the Aztecs, there are few references to urban and architectural models, possibly due to a perceived lack of importance compared with monumental sculptures such as the Sun Stone or the Coatlicue. The best known example of a model is the one illustrated in the book Mexico y sus alrededores published in 1856, where there is a small architectural model in the bottom left corner among a large group of archeological artifacts (Figure 2.31). This model shows a stepped base, a sacrificial stone and a temple on top with its enormous cresting (Schávelzon 1982:361).   Figure 2.31. "Mexican Antiquities," the back of the Teocalli de la Guerra Sagrada and a small single teocalli can be seen in the lower left corner (Lithograph by Decaen 1856).  This same model was reproduced by Desirée Charnay in 1884 and by Chavero in 1889 who utilized it to illustrate the religious architecture of Mexico. In 1910, Newel Warale conducted a study entitled Miniature Clay Temples of Ancient Mexico in which he analyzed a dozen models of the more than 200 that were in the Museo Nacional at the time (Schávelzon 1982:362). To date, no one has continued this research and the whereabouts of many of the models is unknown. That said, some of them were located for this research in public and private collections in the United States of America, the United States of America, Spain and France (Figure 2.32).  75     Figure 2.32. (a) Model in the American Museum of Natural History, New York; (b) model in the Museo de las Américas, Madrid; (c) model in the Musée du quai Branly, Paris (CC BY-NC-SA 4.0).  In 1936, H. D Pollock published the book Round Structures of Aboriginal Middle America that remains a key study on the subject. Pollock analyzed circular structures drawing on various historical sources, manuscripts, paintings and models. In the years that followed, other models were published but always in the context of art not architecture. Decades later, in1960, Ignacio Marquina used some models as inspiration for his reconstructions of the ceremonial precinct of Tenochtitlan, and in 1975, Paul Gendrop and Doris Heyden utilized a photograph of the model by Marquina and other photos of previously unpublished models to illustrate the chapter on Aztec architecture (Schávelzon 1982:362-364). 76   Figure 2.33. Three teocalli models with different representations on the top platform. The first model has a temple, the second a solar deity and the third a single deity (British Museum, CC BY-NC-SA 4.0).  Even though the size, material, quality and detail vary among models, the main characteristics of certain building types can be inferred from all of them. The teocallis always have either a temple or a representation of the gods to which they were dedicated on the top platform; the stairs are flanked by balustrades, and stepped platforms can be seen in some of them (Figure 2.33).  In the few books that were published about pre-Columbian architecture (Marquina 1964; Gendrop and Heyden 1973), models were seen as isolated examples of architectural types but not within the context of an urban plan. This changed in 1995 when nine urban plans were discovered carved in stone at the site now known as Plazuelas in Guanajuato, Mexico (Figure 2.34). This was the first model that represented a specific urban complex in which the carved figures corresponded exactly to the group of buildings found on the site (Schávelzon 2004:11).  77     Figure 2.34. (a) Google Earth view of Plazuelas, (b) model of Plazuelas carved in stone (Photograph by Juan Antonio Siller - CC:BY), (c) aerial view of Plazuelas (Map data: Google Earth).  This finding allowed the researcher to see the Aztec petroglyphs from Acalpixan — known to archaeologists since 1894 — in a different light. In spite of the fact that these petroglyphs have multiple representations of stairs carved on the rocks, they had never been interpreted in the context of urban design.  78   Figure 2.35. Drawing of the model at Acalpixan (Broda 2000:Figure 17).  On this model (Figure 2.35), the main group consists of a complex architectural structure and multiple representations of stairs which have an overlaid pecked cross similar to the known crosses found in Teotihuacan and other places in Mesoamerica. The relevance of this model resides in the fact that it interrelates architecture, urban planning and astronomy, as the pecked crosses served to orient urban complexes and buildings as scholars such as Aveni, Hartung and Buckingham (1978), among others, have demonstrated (Figure 2.36).   Figure 2.36. A collection of pecked cross petroglyphs from Teotihuacan (Aveni 2001:Figure 126).  79  2.10 Oral History  Indigenous scholars such as Jo-ann Archibald have emphasized the interrelationship between place, Indigenous identity and place-based stories and our responsibility as keepers of this cultural knowledge (Archibald 2008:29). Therefore, stories of places passed from generation to generation should also be considered as sources for the study of Aztec architecture and urban planning. An example of this source is the legend of the Tepozteco recorded and analyzed by Vargas-Betancourt (2004) or the research on Aztec and contemporary sacred landscape carried out by ethnohistorians such as Broda (1991a, 1991b).  2.11 Chapter Summary  This chapter demonstrated that number, scope and variety of sources available to study the Aztec culture is extraordinary. Nevertheless, this body of knowledge had not been analyzed from an architectural or urban point of view. Therefore, this chapter presented the architectural and urban representations that were extracted from these sources as well as the relevant information that can be obtained from them. These sources ranged from traditional research material such as pictorial manuscripts, eyewitness accounts by the Conquistadores, chronicles compiled by the missionaries and archaeological evidence, to non-traditional research material like pictorial administrative manuscripts, monumental sculpture, urban and architectural models and oral history. While traditional sources contained material that had to be filtered through the screen of architectural and urban depictions, non-traditional sources contributed a wealth of mathematical and geometric information that was applied to architectural and urban design. In addition, non-traditional sources such as the architectural and urban models demonstrated the interrelation of architecture, urban planning and astronomy (Figure 2.30 and Figure 2.35).  Consequently, this chapter presented most of the sources that were utilized to compile the inventory of Aztec building types (Chapter 3); to describe the concepts of space and time (Chapter 4); and to explain the concepts of astronomy, mathematics and geometry embedded in Aztec architecture and urban planning (Chapter 5). 80  Chapter 3: Aztec Typology  3.1 Introduction  This aim of this chapter is to present a visual sample of the inventory of Aztec architectural types that was done for this research. This inventory was based on the meticulous analyses of the ethno-historical sources carried out in Chapter 1 so as to investigate the common features of each architectural type. To this end, the first section introduces the concept of typology following the ICOMOS Principles for the Recording of Monuments, Groups of Buildings and Sites and discusses the role of typological studies within the context of architectural research in Latin-America. The second section argues the need to define Aztec building types within their cultural context and serves as the antechamber for the third section, a representative sample of probably the most thorough inventory of Aztec building types in Aztec scholarship. Each sub-section presents a dossier of each building type following ICOMOS principles: Nahuatl name, form, cultural functions and examples of a pictographic depiction, a physical representation as well as a plan and photograph of archaeological remains of that building type. The fourth and last section discusses the application of the urban planning principles of Tula and Teotihuacan in the design of Tenochtitlan.  3.2 Aztec Typology  Except for the urban studies of Aztec city-states performed by Smith, the few discussions about Aztec architecture (Marquina 1960; Hardoy 1973; Heyden and Gendrop 1973; Pasztory 1983; Matos 1999; Aguilar Moreno 2006; Uriarte 2010) have mostly concentrated on its individual qualities rather than its common characteristics. A study of Aztec typology [typologies?] was therefore needed in order to understand Aztec architecture.  Since the research performed in the ethno-historical sources had already provided the depictions of Aztec architectural and urban forms, this information was utilized to build an inventory of Aztec building types according to the Principles for the Recording of Monuments, Groups of Buildings and Sites ratified by the 11th International Council on Monuments and Sites 81  (ICOMOS) General Assembly in Sofia, October199617. This document sets out the principal reasons, responsibilities, planning measures, contents, management and sharing considerations for the recording of the cultural heritage, defined in this document as "monuments, groups of buildings and sites of heritage value, constituting the historic or built environment." These principles state that the records should include some or all of the following information:  a) The type, form and dimensions of the building, monument or site; b) The interior and exterior characteristics, as appropriate, of the monument, group of     buildings or site; c) The nature, quality, cultural, artistic and scientific significance of the heritage and its components and the cultural, artistic and scientific significance of:   • the materials, constituent parts and construction, decoration, ornament or inscriptions   • services, fittings and machinery,   • ancillary structures, the gardens, landscape and the cultural, topographical and     natural features of the site; d) The traditional and modern technology and skills used in construction and     maintenance; e) Evidence to establish the date of origin, authorship, ownership, the original design,     extent, use and decoration; f) Evidence to establish the subsequent history of its uses, associated events, structural or     decorative alterations, and the impact of human or natural external forces; g) The history of management, maintenance and repairs; h) Representative elements or samples of construction or site materials; i) An assessment of the current condition of the heritage;  The use of typology for recording and analyzing archaeological sites in Latin-America was proposed by Waisman. She considered "typology as an instrument of architectural historiography                                                  17 Principles for the Recording of Monuments, Groups of Buildings and Sites ratified by the 11th International Council on Monuments and Sites (ICOMOS) General Assembly in Sofia, October 1996:  As the cultural heritage is a unique expression of human achievement; and  As this cultural heritage is continuously at risk; and  As recording is one of the principal ways available to give meaning, understanding, definition and recognition of the values of the cultural heritage; and  As the responsibility for conserving and maintaining the cultural heritage rests not only with the owners but also with conservation specialists and the professionals, managers, politicians and administrators working at all levels of government, and with the public; and  As article 16 of the Charter of Venice requires, it is essential that responsible organizations and individuals record the nature of the cultural heritage. 82  has broad possibilities as a guideline for chronological frameworks, as object of study, as guideline for the classification of the historical material and, finally, as base for the critical-historical analysis of the architectural expressions (Waisman 1998:80)"18.  Consequently, a classification that took into account the particular characteristics of Aztec architectural forms was necessary in order to analyze and evaluate them. However, this typological classification had to be done from a different standpoint; because Western classifications systems should not be applied to Aztec architectural forms. Waisman argued that Latin-American architecture always seemed less when it was analyzed in the context of the original European works and by the criteria developed for them. She rejected the basic Western criteria, such as the division into periods according to stylistic typologies, and claimed that they are irrelevant for local architecture "as they are not original creations of our culture, they are not essential elements for understanding our architecture." Waisman claimed that the analysis of the architectural forms in relation to their environment and to their specific context would necessarily bring different and more precise criteria that enable their evaluation. Furthermore, she suggested creating a system that takes into account the factors that characterize the architectural form, such as its formal, structural and functional typologies, as well as its relationship with the environment.                                                   18 Translated from "La tipología como instrumento de análisis histórico" (Waisman 1998:80):  "La tipología como instrumento de la historiografía arquitectónica presenta varias posibilidades como pauta para la periodización, como objeto de estudio, como pauta para el ordenamiento del material histórico y, por último, como base para el análisis crítico-histórico de los hechos arquitectónicos." 83  3.3 Aztec Building Types  In The Beginnings of Architecture, Sigfried Giedion (1941) dedicated an entire chapter to the differences between ziggurats and pyramids: ziggurats were built inside the cities of the living, while pyramids were built in the cities of the dead; ziggurats had temples on top, while the top of pyramids were totally inaccessible; ziggurats were dedicated to deities, while pyramids were built for kings; ziggurats were integrated to the life of the city, while the pyramids were built in remote locations. Regarding their form, ziggurats were constructed as a series of stepped platforms with a temple on top, while pyramids were built just as pyramids ending in a perfect apex. Regarding their function, ritual sacrifices were performed in ziggurats, while pyramids protected the dead king.   Aztec stepped truncated pyramids with a temple on the upper platform are neither pyramids nor ziggurats, they are their own architectural type: Teocallis.  The term Teocalli was initially used by Batres in 1904 and frequently thereafter by Mexican scholars, however, the word had fallen out of use by 1973 when Heyden and Gendrop published Pre-Columbian Architecture of Mesoamerica. The reasons for this change could be related to the increased involvement of foreign scholars in Mesoamerican archaeology in the second half of the twentieth century, and the urge to disassociate the research of foreign scholars (mostly Anglophone) from the research by Mexican scholars.  Even though these classifications often emerged based on the needs of cross-cultural observations and analyses, they sometimes resulted in inconsistent and geometrically implausible Aztec architectural forms: Single Temple Pyramids, Double Temple Pyramids, and Circular or Round Pyramids. Furthermore, these types ignored the physical and cultural environment in which they were built.  Consequently, in order to define Aztec architecture, an alternative classification of Aztec forms was proposed for this research. This classification is based on three aspects from the ICOMOS Principles for the Recording of Monuments, Groups of Buildings and Sites: type, form and 84  cultural function. Even though this classification was limited by the quantity and quality of information publicly and privately available (especially archaeological records that can vary from primary field notes to exhaustive analyses), it provided a clear and consistent overview of each building type. Its main limitation was that some structures were partially destroyed or were not fully excavated, hence they could fall in more than one architectural type. In these cases, they were placed in the most likely category based on their size and location. In other cases, where there was debate among scholars regarding the type of structure, buildings were placed in the architectural type recognized by the Instituto Nacional de Antropología e Historia (INAH).  The following section consists of a representative sample of the inventory of Aztec building types performed for this research. Each sub-section presents a dossier of each building type following ICOMOS principles: ● Nahuatl19 name (which defines the type name when it refers to an exclusive Aztec form) ● Form (a succinct description of its geometrical form) ● Cultural function ● A collection of pictographic depictions, physical representations, and archaeological evidence  It is neither the intent nor the scope of this architectural research to examine these building types further as some of them have already been discussed within Aztec scholarship, as well as in side references or chapters about Aztec architecture in more general sources (Marquina 1960; Hardoy 73; Heyden and Gendrop 1975; Pasztory 1983; Mangino 1990; Matos 1999; Evans 2004; Fernández and García 2006;Aguilar 2006; Smith 2008; Manzanilla 2009; Uriarte and Toca 2010). However, this inventory can be viewed as one of the first attempts to establish an area of study for Aztec architectural and urban research.                                                   19 Nahuatl entries come from the Nahuatl Dictionary, a Wired Humanities Project supported by the National Science Foundation and the National Endowment for the Humanities, and major input from John Sullivan and the Zacatecas Institute for Teaching and Research in Ethnology, and the European Research Council, University of Warsaw, and Universidad de Sevilla. 85  3.3.1 Single Temple Teocalli  Nahuatl name [Single Temple] Teocalli (Figure 3.1) English Translation: A temple or church (synonymous with teopan); or, something smaller, such as a chapel; or, a devotional building in a private residence.  Form A stepped truncated rectangular base pyramid with one stairway and a single chamber on top.  Cultural function Symbolic form of a mountain utilized by priests and some members of the nobility to perform rituals and ceremonies (including fasting, vigils, offering of prayers and hymns, as well as sacrificial rituals involving foodstuffs, birds, animals, war captives, and self-let blood) in order to communicate with the gods on behalf of the community (Kowalski 2006).   86  Single Temple Teocalli (continued)   Depiction of Single Temple Teocalli in the Mapa de Cuauhtinchan No. 2 (Figure 2.17). Single Temple Teocalli model (Museo Regional de Puebla, CC-BY-NC-SA 2.0).   Single Temple Teocalli "C" in Tula (Photograph by Javier García Muñoz - CC:BY). Single Temple Teocalli "C" plan, Tula (López Austin and López Luján 2009:Figure 2). Figure 3.1. From left to right, examples of the Single Temple Teocalli architectural type: depiction within a codex, small scale model, archaeological remains and plan view.  87  3.3.2 Double Temple (or Twin Temple) Teocalli  Nahuatl name Double Temple Teocalli (Figure 3.2) English Translation: A temple or church (synonymous with teopan); or, something smaller, such as a chapel; or, a devotional building in a private residence.  Huey Teocalli English Translation: Great Temple  Form A stepped truncated rectangular base pyramid with two stairways and two chambers on top; one temple is associated with Tlaloc and the other to Huitzilopochtli.  These structures were  usually built in several stages and are considered to be a unique architectural type as the birth of Huitzilopochtli was enacted on its temples.  Cultural function Symbolic form of a mountain utilized by priests and some members of the nobility to perform rituals and ceremonies (including fasting, vigils, offering of prayers and hymns, as well as sacrificial rituals involving foodstuffs, birds, animals, war captives, and self-let blood) in order to communicate with the gods on behalf of the community (Kowalski 2006).   88  Double Temple (or Twin Temple) Teocalli (continued)   Depiction of Double Temple Teocalli of Tetzcoco in the Codex Ixtlilxochitl, folio 112v (Figure 2.12). Double Temple Teocalli model (American Museum of Natural History, CC-BY-NC-SA 4.0).   Double Temple Teocalli, Teopanzolco (Photograph by Raul Muñiz - CC:BY). Double Temple Teocalli plan, Teopanzolco (Marquina 1964:Figure 63). Figure 3.2. From left to right, examples of the Double Teocalli architectural type: depiction within a codex, small scale model, archaeological remains and plan view.  89  3.3.3 Circular Base Teocalli  Nahuatl name Circular Base Teocalli (Figure 3.3) English Translation: A temple or church (synonymous with teopan); or, something smaller, such as a chapel; or, a devotional building in a private residence  Form A stepped truncated circular base cone with one stairway and one chamber on top  Cultural function Symbolic form of a mountain utilized by priests and some members of the nobility to perform rituals and ceremonies (including fasting, vigils, offering of prayers and hymns, as well as sacrificial rituals involving foodstuffs, birds, animals, war captives, and self-let blood) in order to communicate with the gods on behalf of the community (Kowalski 2006). This particular form is associated with Quetzalcoatl, the Feathered Serpent deity, who had multiple functions and aspects such as creativity and fertility; the Feathered Serpent was also known as Ehecatl, or Wind, so it is sometimes called Ehecatl Quetzalcoatl (Nicholson 1975).   90  Circular Base Teocalli (continued)   Depiction of Circular Base Teocalli in the Codex Azcatitlan, plate 059-064_08 (Figure 2.8). Circular Base Teocalli model (Museo Nacional de Antropología CC-BY-NC-SA 4.0).   Circular Base Teocalli, Tlatelolco (Photograph by César Tenorio - CC:BY). Circular Base Teocalli, Tlatelolco (Proyecto Tlatelolco - INAH). Figure 3.3. From left to right, examples of the Circular Base Teocalli architectural type: depiction within a codex, small scale model, archaeological remains and plan view.  91  3.3.4 Warriors / Priests Precinct  Nahuatl name Warriors / Priests Precinct in Teocalli (Figure 3.4)  Teocalli English Translation: A temple or church (synonymous with teopan); or, something smaller, such as a chapel; or, a devotional building in a private residence.  Form An L-shaped plan precinct constructed north of the Huey Teocalli with two stairs at the western end; and several interior rooms; there was probably another Teocalli precinct at the south of the Huey Teocalli, although no archaeological evidence has been found.   Cultural function The immediate proximity of this warrior precinct to the Huey Teocalli demonstrates the sacred character of warriors in warfare Carrasco 145); it was a place where elite warriors gathered, "no one could enter that house of knightly order unless he was a warrior or a son of a known knight" (Durán 1994:192).   92  Teocalli (Priests and/or Warriors) Precinct (continued)  Eagle Warriors Precinct within the Main Double Teocalli of Tetzcoco in the Codex Ixtlilxochitl, folio 112v (Figure 2.12).   Warriors Precinct within the Huey Teocalli (Templo Mayor) of Tenochtitlan (Photograph by George and Eve DeLange - CC:BY). Plan of the Warriors Precinct within the Huey Teocalli (Templo Mayor) of Tenochtitlan (Umberger and Klein 1993:304). Figure 3.4. From top to bottom, examples of the Warriors Precinct within the Teocalli architectural type: depiction within a codex, small scale model, archaeological remains and plan view.  93  3.3.5 Tzompantli  Nahuatl name Tzompantli (Figure 3.5) English Translation: Skull rack  Form An elongated rectangular base characterized by the "exhibition of human skulls (either real or sculpted) in horizontal rows"; the real human skulls were held along a series of wooden frames made of horizontal crossbeams connected to a series of vertical posts; some scholars suggest that the platforms with sculpted human skulls held a wooden frame for real human skulls on top.  Cultural function Besides utilizing them to display the skulls of ritualistically-executed victims, scholars have offered several interpretations of their meaning: Matos (1988) associates them with the Land of the Dead and Carrasco (1991) with Tezcatlipoca, while Hassig (1988) believes they were used to intimidate enemies (Mock 2001).   94  Tzompantli (continued)   Depiction of Tzompantli in the Book of the Gods and Rites by Durán (Biblioteca Nacional de España, CC-BY-NC-SA 4.0). Depiction of Tzompantli (front view) in the Codex Azcatitlan, plate 059-064_22 (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0).   Tzompantli in the Huey Teocalli of Tenochtitlan (Photograph by Ihiro Alfonso - CC:BY). Tzompantli Plan, Huey Teocalli of Tenochtitlan (Matos 1988b:Figure 34). Figure 3.5. From left to right, examples of the Tzompantli architectural type: depiction within a codex, small scale model, archaeological remains and plan view. 95  3.3.6 Tlatchtli  Nahuatl name Tlatchtli (Figure 3.6) English Translation: Ball court  Form I-shaped court with raised inclined platforms along the vertical axis and a vertical disk in the middle of these platforms.  Cultural function Ullamaliztli, the name of the ancient Mesoamerican ball game in Nahuatl, was played in the Tlatchtli; the ball court mirrored the celestial ball court as the western axis symbolizes the underworld through which the Sun, represented by the ball, passes each night, thus the game reenacted the "battle between the Sun and Moon, or the gods of youth and maturity, each vying for supremacy" (Aguilar 2007:361-362).   96  Tlatchtli (continued)   Depiction of Tlatchtli, folio 80 in the Codex Magliabechiano, Nuttal facsimile (Biblioteca Nazionale Centrale di Firenze, CC-BY-NC-SA 4.0). Tlachtli model carved on rock (Photograph Museo de Sitio de San Miguel Ixtapan, Tejupilco, Mexico).   Tlachtli, Tula (Photograph by Ramón Hernández - CC:BY).  Tlachtli, Tula (Healan 2012:Figure 6). Figure 3.6. From left to right, examples of the Tlachtli architectural type: depiction within a codex, small scale model, archaeological remains and plan view.  97  3.3.7 Momoztli  Nahuatl name Momoztli (Figure 3.7) Platform or raised altar for sacrifices and displays in pre- conquest style; mound, platform, etc., in colonial times.  Form This type encompasses a wide variety of small rectangular base and circular base low platforms with a stairway in the front, built individually or in groups along public locations. Noguera describes them either as small altars erected at the junction of roads or as small platforms that were placed in front or at the sides of a temple (Noguera 1973:111). Hence this typological study made the distinction between Momoztlis built around temples and the Central Momoztlis placed at the centre of major axes. Cultural function There is scarcely any research about Momoztli as the interpretations of scholars vary from being a seat for the Emperor to the Teocalli at Castillo de Teayo (Olivier 2003:320). However, they are abundantly present in pictographic and written sources within the context of ceremonies, which suggests that they were utilized by priests, nobility and commoners alike. Durán describes them as a place where gods sat and rested (2003:93).    98  Momoztli (continued)   Depiction of Momoztli in Codex Borgia, plate 42 (Biblioteca Apostolica Vaticana, CC-BY-NC-SA 4.0). Digital reconstruction of Momoztli (Templo Rojo) in the ceremonial precinct of Tenochtitlan (Model by Michelle de Anda, Proyecto Templo Mayor-INAH).    Momoztli (Templo Rojo) in the ceremonial precinct of Tenochtitlan (Proyecto Templo Mayor-INAH). (sh3b) "Templo Rojo" Momoztli, Great Teocalli, Tenochtitlan (Matos 1988b:Figure 34). Figure 3.7. From left to right, examples of the Momoztli architectural type: depiction within a codex, digital reconstruction, archaeological remains and plan view. 99  3.3.8 Central Momoztli  Nahuatl name Central Momoztli (Figure 3.8) Platform or raised altar for sacrifices and displays in pre- conquest style; mound, platform, etc., in colonial times.  Form Small square base platform with stairs on its four sides found at the centre of ceremonial precincts.  Cultural function Except for the study performed by Noguera (1973), there is scarcely any research about Central Momoztli. However, pictographic and archaeological evidence suggests they were utilized by priests to perform rituals and ceremonies at the centre of temple precincts at an urban level and at the centre of patios at a domestic level.   100  Central Momoztli (continued)   Depiction of Central Momoztli (rotated 90 degrees), Codex Borbonicus, folio 36 (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0). Depiction of Momoztli, Primeros Memoriales, folio 268r (Real Biblioteca de Madrid, CC-BY-NC-SA 4.0).   Central Momoztli, Tula (Photograph by Antonio Rafael- CC:BY). Momoztli, Tula (Healan 2012:Detail within Figure 6). Figure 3.8. From left to right, examples of the Central Momoztli architectural type: depictions within codices, archaeological remains and plan view.  101  3.3.9 Quauhxicalli and Temalacatl  Nahuatl name Quauhxicalli (according to Molina and Sahagún) A wooden pan or vessel (Molina); eagle vessel for containing hearts and blood of sacrificial victims (Sahagún).  Temalacatl (according to Molina and Sahagún) Circular, flat, sacrificial stone.  Quauhxicalli (according to Berdan) Flat platform with or without a central cavity (Berdan 97).  Temalacatl (according to Berdan) Similar but had a bar or ring in the centre for the attachment of captive warriors during gladiatorial sacrifice (Berdan 97).  Illustrations in Figure 3.9. Form A circular base platform.  Cultural function Symbolic form of the Sun utilized for gladiatorial sacrifice.   102  Temalacatl (continued)   Depiction of Temalacatl in the Historia de las Cosas de la Nueva España, folio 70r (Biblioteca Nacional de España, CC-BY-NC-SA 4.0). Temalacatl, ex Archbishopric's Palace Stone (Museo Nacional de Antropología-INAH).   Depiction of Quauhxicalli, Florentine Codex, volume 2, folio 635 (Biblioteca Medicea Laurenziana, Firenze, CC-BY-NC-SA 4.0). Quauhxicalli, Plaza Manuel Gamio, Tenochtitlan (Proyecto Templo Mayor-INAH). Figure 3.9. From left to right, examples of the Temalacatl architectural type: depictions within a codex, monumental sculpture and archaeological remains. 103  3.3.10 Calmecac  Nahuatl name Calmecac (Figure 3.10) English Translation: School, primarily for noble youths (mostly boys), that offered religious training.  Form A rectangular patio surrounded by several interior rooms.  Cultural function A school where priests taught noble youths religion, mythology, history, calendrics, writing, engineering and law, along with thorough military training (López Austin and López Lujan 2001:221-223).   104  Calmecac (continued)   Depiction of Calmecac, Codex Mendoza, folio 61r (Bodleian Library, CC-BY-NC-SA 4.0). Depiction of Calmecac, Primeros Memoriales, folio 252v (Real Biblioteca de Madrid, CC-BY-NC-SA 4.0).   Calmecac under the building of the Centro (Museo de Sitio del Centro Cultural de España en México). Remains of 2.38 metres tall crenels  from the roof of the Calmecac (Photograph by Boris de Swan-Raíces). Figure 3.10. From top to bottom, examples of the Calmecac architectural type: depictions within codices and archaeological remains.  105  3.3.11 Coatepantli of Huey Teocalli and Perimeter Wall of Ceremonial Precinct  Nahuatl name Coatepantli (Figure 3.11) English Translation: Serpent-wall, snake-wall, a ceremonial wall decorated with snakes.  Perimeter Wall of Ceremonial Precinct (Figure 3.11) Even though there has been confusion among scholars between the coatepantli of the Huey Teocalli and the perimeter wall of the ceremonial precinct, ethnohistorical sources and archaeological excavations have confirmed that these were two different architectural types.   Form The coatepantli is a row of snakes in the forecourt or around the Huey Teocalli, while the perimeter wall is a platform that surrounds a ceremonial precinct (Boone 1987:59).  Cultural function The snakes of the coatepantli symbolize the Earth and are one of the most important symbols in Mesoamerica. Since the Aztecs saw their world as a flat disk where the Huey Teocalli was the centre of the axis mundi, the snakes represent the great body of Earth itself. Furthermore, Huey Teocalli is an embodiment of Coatepec, "Snake Mountain," where the god Huitzilopochtli was born.  The perimeter wall of the ceremonial precinct separated the sacred space of the ceremonial precinct from the profane space surrounding it (Matos 1987:200).   106  Coatepantli of Huey Teocalli and Perimeter Wall of Ceremonial Precinct (continued)   Depiction of the Coatepantli in the Huey Teocalli, Book of the Gods and Rites (Biblioteca Nacional de España, CC-BY-NC-SA 4.0). Coatepantli of the Huey Teocalli in Tenochtitlan (Photograph by Maghenzani - CC:BY).    Depiction of the Perimeter Wall, Codex Aubin, plate 035-036-41v (British Museum, CC-BY-NC-SA 4.0). Perimeter Wall in Tlatelolco (Photograph by Renata Martínez- CC:BY). Figure 3.11. From left to right, examples of Coatepantli and Perimeter wall of ceremonial precinct architectural type: depictions within a codex and archaeological remains. 107  3.3.12 Nobility Dwellings: Calli and Tecpan  Nahuatl name Calli (Figure 3.12) English Translation: House, structure, container; also, a calendrical marker.   According to Sahagún: Tlatocacali: ruler’s house Tequioacacali: war leader’s council house Tecali: palace court house Pilcali: nobleman’s house Achcauhcali : constable’s house  Tecpan English Translation: Unit of social organization of high nobles; noble house; royal palace, government building.   Form A rectangular patio dominated by a dais room and surrounded by several rooms with different civil and military functions.  Cultural function The Tecpan reflects the societal structure of the Aztecs. They were "extraordinarily hierarchical and richly nuanced, with administrative places, pleasure palaces, and mansions, all designed to cosset their noble denizens, and advertise themselves to the world as seats of authority" (Evans 2004:7).   108  Nobility Dwellings: Calli and Tecpan (continued)   Depiction of the Palace of Motecuhzoma in the Codex Mendoza, folio 69r (Bodleian Library, CC-BY-NC-SA 4.0). Enhanced copy of the depiction of the Palace at Tetzcoco in the Mapa Quinatzin (Bibliothèque Nationale de France CC-BY-NC-SA 4.0).   Depiction of Nobility Dwelling in Mapa de Cuauhtinchan No. 2 (Figure 2.17). Depiction of Nobility Dwelling, Florentine Codex, volume 3, folio 802 (Biblioteca Medicea Laurenziana, Firenze CC-BY-NC-SA 4.0). Figure 3.12. Examples of Nobility Dwellings architectural type within codices.  109  3.3.13 Commoners Dwellings: Calli  Nahuatl name Commoner Calli (Figure 3.13) English Translation: House, structure, container; also, a calendrical marker.   According to Sahagún: Callli: house or room Caltepiton: small house Caltontli: small house Caltzintli: small (or honored) house  Form Form varies from a cave, to a single rectangular room, to a patio surrounded by rooms along two, three, or four of its sides.  Cultural function The form, spatial distribution and construction materials reflect the societal structure of the Aztecs.   110  Commoner Dwellings: Calli (continued)   Depiction of House (wood walls, straw roof), Florentine Codex, volume 3, folio 799 (Biblioteca Medicea Laurenziana, Firenze CC-BY-NC-SA 4.0). Depiction of House, Florentine Codex, volume 3, folio 801 (Biblioteca Medicea Laurenziana, Firenze CC-BY-NC-SA 4.0).   Depiction of House, Florentine Codex, volume 2, folio 499cd5 (Biblioteca Medicea Laurenziana, Firenze CC-BY-NC-SA 4.0). Plan of the house and property title located in Huexocolco (Archivo General de la Nación CC-BY-NC-SA 4.0). Figure 3.13. Examples of Commoner Dwellings architectural type within a codices and administrative-legal documents. 111  3.3.14 Temazcalli  Nahuatl name Temazcalli (Figure 3.14) English Translation: A sweat house or sweat bath.  Form A rectangular room with a circular dome.  Cultural function In Mesoamerica, a Temazcalli is a vapour bath for therapeutic purposes; it is a representation of a cave, a symbol of the beginning of life.   112  Temazcalli (continued)   Depiction of Temazcalli, Codex Aubin, folio 035-036_24v (British Museum, CC-BY-NC-SA 4.0). Depiction of Temazcalli, Codex Magliabechiano, folio 77r (Biblioteca Nazionale Centrale di Firenze CC-BY-NC-SA 4.0).   Depiction of Temazcalli, Codex Tudela, folio 62r (Museo de América, Madrid CC-BY-NC-SA 4.0). Depiction of Temazcalli, Florentine Codex, volume 3, folio 675 (Biblioteca Medicea Laurenziana, Firenze CC-BY-NC-SA 4.0). Figure 3.14. Examples of the Temazcalli architectural type within codices.  113  3.3.15 Gardens and pools  Nahuatl name Xoxochitlatli (Figure 3.15) English Translation A garden.  Acaxitl (Figure 3.15) English Translation  Pool, watering trough.  Form Gardens were sacred spaces modeled to convey the idea of a terrestrial paradise.  Cultural function Aztec cosmovision was reflected in the layout of the gardens regardless of their size. The largest gardens were built around ritual places such as mountains, springs and caves, while there were small gardens built beside the palaces of the nobility that held also a wide variety of flora, fauna and pools.  Gardens were not only for the enjoyment of the Emperor and royal nobles, but were also multi-purpose botanical gardens associated with the curing of physical and spiritual ills as they also kept a wide array of ornamental, aromatic and medicinal plants. The pools were filled with spring water that came from sophisticated aqueducts and contained several types of fish and waterfowl. There were royal gardens in and near Tenochtitlan, Chapultepec, Iztapalapa, el Peñón and Tetzcoco, as well as in more distant locations such as Tetzcotzinco and Huaxtepec (Aguilar 2007:225, Avilés 2006:143, Granziera 2001:208).    114  Gardens and Pools (continued)   Depiction of Gardens and pool in Chapultepec, Historia de las Cosas de la Nueva España, folio 11r (Biblioteca Nacional de España, CC-BY-NC-SA 4.0). King's baths in Tetzcotzinco garden (Photograph by Lia Sali - CC:BY).  Tetzcotzinco plan, also known as "Nezahualcoyotl's baths" (Evans 2010:Figure 15.3). Figure 3.15. Clockwise, examples of the Gardens and Pools architectural type: depiction within a codex, archaeological remains and plan.  115  3.3.16 Markets  Nahuatl name Tianquiztli (Figure 3.16) English Translation: Market, place of commerce.  Form Large open-air markets were located in close proximity to the main ceremonial precincts of cities; smaller open-air markets were located throughout the city as Cortés describes: "This city has many plazas where there are ongoing markets and dealings to buy and sell…"20  Cultural function Aztec markets varied in size and the type of products sold. Besides the markets that supplied food, there were others who were specialized in certain products. Azcapotzalco was dedicated to the sale of slaves; Cholula traded only jewelry, gems and the feathers of birds; Tetzcoco focused on clothing, cups and earthenware; and Acolman sold dogs for domestication and meat (Attolini 436).                                                    20 Translated from Cortés (1866:103):  Tiene esta ciudad muchas plazas, donde hay continuo mercado y trato de comprar y vender…  116  Markets (continued)  Depiction of Market (feathers, gold, precious stones, and textiles) , Florentine Codex, book 3, chapter 9 (Biblioteca Medicea Laurenziana, Firenze CC-BY-NC-SA 4.0).   Merchants buying feathers, Florentine Codex, book 2, folio 742 (Biblioteca Medicea Laurenziana, Firenze CC-BY-NC-SA 4.0).  Weaver selling textiles and baskets in market (Photograph by Montaldo Vera - CC:BY). Figure 3.16. From top to bottom, examples of the Market architectural type: depictions within a codex and a contemporary market.  117  3.3.17 Engineering Works - Chinampa, Dams, Embankments, Dykes, Roads, Piers, Canals, and Bridges  Nahuatl name Chinampa (Figure 3.17) English Translation: A long narrow extension of farmland built by human hands and stretching into the lakes around Mexico City.  Axoxōhuīlli English Translation: dam, lake.  Metepantli English Translation: Terrace, embankment, or a sloping semi-terrace field.  Atenamitl (Figure 3.17) English Translation Parapet, eve or the sides of a rooftop; wall; or, dyke.  Calotli English Translation The road or path that leads to some house; street.  Acaltecoyan English Translation seaport or an embarkation site [pier].  Acallotli English Translation Canal. 118   Aquappanahuaztli English Translation A wooden bridge.  Form Varied, depending on function.  Cultural function To control frequent flooding, increase agricultural areas and facilitate communication within the complex lake system in the Basin of Mexico, the Aztecs developed sophisticated engineering and hydraulic works. These works included chinampas, dams, embankments, dykes, roads, piers, canals and bridges, among others.   119  Engineering Works - Chinampas (continued)   Depiction of chinampas (canals, roads and two Teocallis in upper right), Plano Parcial de la Ciudad de Mexico (Biblioteca Nacional de Antropología e Historia CC-BY-NC-SA 4.0). Depiction of properties including house and chinampas, Propiedades en Xochimilco (Archivo General de la Nación CC-BY-NC-SA 4.0).   Depiction of property including house and chinampas, San Juan Tepiztlan (Archivo General de la Nación CC-BY-NC-SA 4.0). Aerial view of Chinampas, Xochimilco (Photograph by Imágenes Aéreas de México - CC:BY). Figure 3.17. From top to bottom, examples of Chinampas: depictions within a codex and administrative-legal documents and contemporary chinampas. 120  Engineering Works - Aqueducts and Dykes (continued)   Aqueduct from the spring of Chapultepec to Tenochtitlan, Codex Panes Abellán, vol. 4, folio 148 (Archivo General de la Nación CC-BY-NC-SA 4.0). Aqueduct section from Moctezuma’s pool to the Cincalco cave, Chapultepec (Photograph by Alfonso Marroquin - CC:BY).   Dyke of Nezahualcoyotl to separate Lake Texcoco from Xochimilco, Nuremberg map (Newberry Library CC-BY-NC-SA 4.0). Remains of the Dyke of Nezahualcoyotl (Photograph by Benjamin Arredondo - CC:BY). Figure 3.18. From left to right, examples of Aqueducts and Dykes: depiction of aqueduct within codex and contemporary aqueduct; depiction of dyke within map and contemporary dyke. 121  3.4 Aztec Urban Forms  The influence of the urban layouts of Teotihuacan and Tula has been thoroughly discussed in Aztec scholarship (Marquina 1964; Cobean, Mastache, and Healan 1989, 1995, 2003; López Luján 1995, 2006, 2009; Matos 1999; Guilliem 2003; Smith 2008; López Austin and López Luján 2009). These sites were even studied by the Aztecs, who utilized them as sources for Aztec identity. Teotihuacan was the place where time began and Tula was the source of power to justify its right to military expansion. They drew upon Teotihuacan and Tula to design their city, which were considered sacred sites that were visited, honoured and deprived of the vestiges of their ancient glories by the Aztecs and their contemporaries (López Luján and López Austin 2009: 411). By borrowing from the past, they validated their rights to power as heirs of these ancient cultures. Even though Teotihuacan was already in ruins, its urban design and the inter-relationship of its architecture with the landscape were still evident, so the Aztecs laid out Tenochtitlan following the same urban principles. The division of Teotihuacan into four quadrants, defined by the urban north-south urban axis of the Avenue of the Dead and east-west axis of the Pyramid of the Sun, were reflected on the division in quarters of Tenochtitlan (Matos 1981:260). Tula, with its architecture, sculptures, paintings and ritual objects, was a model for Tenochtitlan. López Austin and López Luján summarize it in these words:  There is evidence that one incentive for copying Tula must have been political: the ostentatious display showing that the Mexica capital was the successor of the former city’s power and held an unbroken legitimacy. However, other evidence suggests much more profound causes: the use of forms that invited divine beings to occupy their space (López Luján and López Austin 2009:411-412).  Teotihuacan and Tula shared similar Mesoamerican planning principles such as clockwise orientation east of north of its main urban axes, orthogonal grid planning and ceremonial plazas, as well as some Mesoamerican architectural building types. Although the main layout of Teotihuacan followed a central axis —the Avenue of the Dead— it culminated in the plaza of the Pyramid of the Moon, and the perpendicular axis was dominated by the Pyramid of the Sun. Although Tula had three formal plazas—the south small plaza (unexcavated), the central public plaza and the north plaza (dominated by the Tlachtli)—its urban arrangement was characterized by a central ceremonial plaza, with the main teocalli on the east and other buildings in an 122  orthogonal layout. In the urban arrangements of both Teotihuacan and Tula, the two main teocallis are perpendicular to each other, with the larger teocalli facing east. This axial plan arrangement can also be found in ethno-historical sources where this arrangement served as an organizing principle of the ceremonies that were organized in these urban spaces (Figure 3.19).    Depiction of complex assemblage with axial plan (Titl ritual), Codex Borbonicus, plates 35 and 36 (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0). Depiction of complex assemblage (ceremonial precinct of Tenochtitlan) with axial plan, Codex Aubin, plate 035-036-41v (British Museum, CC-BY-NC-SA 4.0). Figure 3.19. Examples of the central ceremonial plaza plan characterized by a major teocalli serving as a focal point in an orthogonal layout within a plaza.  123  3.5 Chapter Summary  This chapter demonstrated that the study of Aztec architectural types is necessary for the understanding of Aztec architecture and urban planning. Even though some of these architectural types had already been in use in Mesoamerican architecture, the Aztecs appropriated their forms and meanings into the design of their buildings. Therefore, an inventory of Aztec architectural types—based on the ICOMOS Principles for the Recording of Monuments, Groups of Buildings and Sites—was carried out so as to define the common characteristics of each building type, particularly the unique Aztec double temple teocalli architectural type. This inventory helped to define Aztec architectural types in traditional sources such as codices and archaeological remains, and non-traditional sources such as pictorial-administrative manuscripts and sculpture. It also validated the double temple teocalli as an Aztec architectural type, which was found in seven main Aztec cities: Tenochtitlan, Tlatelolco, Tenayuca, Santa Maria Acatitlan and Teopanzolco as archeological remains, and Texcoco and Tlacopan as pictorial representations.  Regarding Aztec urban forms, this chapter presented the influence of the urban design of Teotihuacan and Tula in the layout of Tenochtitlan as several scholars have argued. These planning principles included the clockwise east-of-north deviation of the urban axes; the orthogonal planning or the urban grid; the organization of the main buildings into a central axial plan; the utilization of common Mesoamerican architectural types; and the orientation of the larger teocalli along the east-west urban axis.  Consequently, the findings of this typological research provided the architectural and urban information that were taken into consideration for the archaeoastronomical analyses of the Aztec sites where a double temple teocalli—the most distinct Aztec architectural type—has been excavated (Chapter 6). 124  Chapter 4: The Aztec Cosmological Concept of Space and Time  4.1 Introduction  The aim of this chapter is to introduce the Aztec cosmological concepts of space and time in order to understand how they were embedded in Aztec architecture and urban planning, as the research carried out in the ethnohistorical sources (Chapter 2) and the typological studies (Chapter 3) revealed their intrinsic connections . The first section presents the concept of cosmovision and its relationship with the landscape, skyscape and religious beliefs the embedded in the symbolism the Huey Teocalli according to ample research done in this area of Aztec scholarship. The second section narrates two fundamental stories in Aztec religion and mythology: the creation of the world and the birth of Huitzilopochtli —god of Sun, fire, war and patron deity of the Aztec— and the relationship of these myths with the four directions, the movement of the Sun across the sky and the symbolic meaning of mountains. The third section describes the concept of space and time in the Aztec calendar. The fourth section describes how these cosmological concepts were integrated into the sacred landscape comprised of mountains, caves and bodies of water, and emphasizes the importance of Tlaloc — god of rain, water and lighting— and the rituals performed on Cerro Tlaloc. The last section introduces the research carried out in the field of high mountain archaeology and its relevance for the understanding of the sacred landscape in the Valley of Mexico.  4.2 The Concept of Cosmovision  Several scholars such as Calnek, Arnold, Broda, Townsend, and Aveni agree that in order to comprehend the arrangement and planning in the ceremonial space of Tenochtitlan, one must "become familiar with the landscape and skyscape of both the city and the space in the Valley of Mexico" and recognize that the reenactment of religious myths took place within this environment as certain ceremonies were required "to take place in both the proper spatial and temporal order" (Aveni 1999: 58).  125  Thus, to fully understand the symbolism embedded in Aztec architecture and urban planning, it is necessary to understand both the physical space and the Aztec multifaceted religious system that consisted of various, and at times, contradictory myths, as well as a multiplicity of gods who were sometimes venerated as multiple personifications of the same gods. This religious system was connected by some shared concepts, the intrinsic sacredness of all aspects of life and a cyclical pattern of transformation (Pasztory 1983:56).  These shared concepts were founded on two basic characteristics of ancient societies: agriculture and rain, which have economic importance to society as they are the main basis of agricultural activity, which in turn is closely related to seasonal changes. Thus, it was necessary to understand the cycles of nature to forecast different seasons. The basic concept in the worldview of the Aztecs is the structured order of the universe, in which nature was created out of dual opposing forces: day and night, light and dark, cold and heat. This conception of the universe was closely associated with the origin of all things: the gods, the stars, the Earth and humankind. Matos defines this set of ideas and its explanation as cosmovision (Matos 1989:95).  4.3 The Conception of Space in Aztec Cosmology and Mythology  A creation myth that illustrates the concept of the world divided in four quarters is the story of Cipactli, the original being, the primordial feminine sea monster that swam in the vastness of the waters. Two gods cut her body in two parts; they built the heavens with one part and the underworld with the other part. The heavens were fertilizing and giving, the underworld producing and receiving. To separate the two parts, the gods placed five posts, one at the center and the remaining four at each corner of the Earth. The intermediate part created by this separation was the world inhabited by humankind. Everything was grouped in accordance to the four cardinal points of the compass and the central direction of up and down. Therefore, the numbers four and five were extremely important and manifested as four quadrants and five directions. These four directions and corners of the Earth are religious symbols for the cardinal points. This myth is complemented by the myth of Ometecuhtli and Omecihuatl (Figure 4.1), the supreme divine couple who resided in Omeyocan, where they engendered four divinities: Xipe or the red Tezcatlipoca, the black Tezcatlipoca, Quetzalcoatl and Huitzilopochtli. After 600 years, 126  the two Tezcatlipocas entrusted to their younger brothers, Quetzalcoatl and Huitzilopochtli, fire, a half Sun, the first humans, the calendar, the lords of the underworld, twelve other heavens, the gods of water and the Earth and the first humans (Graulich 2006b) These four gods are the lords of the four directions of the Earth, or holders from heaven, and are associated with four colours: red to east, black to north, blue to south, and white to west.   Figure 4.1. The aged primordial couple, Oxomoco engaged in divining with maize kernels and her partner, Cipactonal, holding an incense container and burner, Codex Borbonicus folio 19 (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0).21  Meanwhile, the god Huitzilopochtli also has great importance as a Sun god. The myth of Huitzilopochtli recounts how the goddess Coatlicue -Earth- was sweeping the temple stairs on the hill of Coatepec, when she was supernaturally impregnated by a little ball of feathers that floated down from the sky and that she tucked away next to her bosom. Her other children, her daughter, Coyolxauhqui -Moon- and his four hundred brothers, Centzon Huitznahua -the stars- were angered by this fact and decided to kill her. Coatlicue was saddened by the decision of her                                                  21 "A passage in Book 4 (The Soothsayers) of the Florentine Codex links this ancient pair to the invention of the Tonalamatl [ritual calendar], adding that their painted images adorned this book. A mural with a similar scene was recently unearthed in the Templo Mayor of Tlatelolco, painted on one side of a rectangular structure known as the Calendar Templo, which features reliefs of the days signs of the first three trecenas of the tonalpohualli carved around the remaining sides" (Quiñones Keber). 127  children, but her son Huitzilopochtli -the Sun- who was in her womb consoled her and offered to defend her. When the Moon and stars came to slaughter Coatlicue, the Sun Huitzilopochtli was born fully armed for war with a fire serpent called Xiuhcoatl (Figure 4.2 (a)), with which he decapitated his sister, and pushed her down from the top of Coatepec hill. As her body fell, her body dismembered with each turn (Figure 4.2 (b)). He then turned to the Centzon Huitznahua and put them to flight from the summit of Coatepec Hill (Matos 1988b:40-42).   (a)  (b) Figure 4.2. (a) Huitzilopochtli armed for war with a fire serpent called Xiuhcoatl, Codex Tovar, 1a (Jean Carter Library at Brown University, CC-BY-NC-SA 4.0); (b) Coyolxauhqui Stone found at the Huey Teocalli (Museo del Templo Mayor-INAH).  Matos considers this myth particularly important for different reasons: it represents the daily struggles of the Sun against the Moon and stars; it explains the celestial phenomenon in which the Moon dies every month and is born in phases; it gives a theological justification to the warlike character of the Aztecs, as its main god, Huitzilopochtli "was created precisely to do battle" (Matos 1988b:42).  These myths, as well as the interpretation by Eduard Seler and Alfredo López Austin of the layers of heavens, Earth and underworld depicted in the Codex Vaticanus A, reveal the Aztec conception of the universe (Figure 4.3). "This structured way of viewing the heavenly bodies and 128  the Earth as well as the placement of the gods and of man himself in the cosmos, forms part of their complex philosophy and religion, their worldview. In this view, the universe consists of three levels: the highest or celestial level; the central or terrestrial level; and the lowest level or the underworld" (Matos 1988b:123).   Figure 4.3. The deity Ometeotl and the layers of the heavens (left); two lowest layers of heavens, above the layer of the Earth and the underworld, Codex Vaticanus A/Loubat, folios 1v and 2r (FAMSI CC-BY-NC-SA 4.0).  The celestial was further divided in thirteen layers or heavens. The last double heaven, the twelfth and thirteenth, known as Omeyocan, the "Place of Duality," was inhabited by Ometecuhtli and Omecihuatl: the eleventh, the red sky; the tenth and ninth, yellow and white. Down in the eighth, called yztapol nanazcaya, interpreted as "place where the corners are of obsidian knives," is the place of Tonacatecuhtli and where tempests are said to form. The seventh, the blue sky, is where Huitzilopochtli lives. The sixth heaven is green; the fifth is considered the "rotating heaven" where the comets and stars move; the fourth is inhabited by the planet Venus or, according to some sources, Uixtocihuatl, the goddess of salt waters; the third is 129  the path of the Sun, Tonatiuh, and is the heaven where the Sun leaves each day to cross the sky; the second heaven is the place of the stars, the Milky Way, inhabited by Citlalatonac and Citlalicue, both gods of the night sky; and finally, the heaven closer to Earth is inhabited by the Moon and clouds (González Torres 1975:21-34; Matos 1988b:124).  The terrestrial level was where humans live, and from the centre of this level emanate the four world directions, each identified with a creator god, a calendrical symbol, a colour and a plant as illustrated in the Codex Fejérváry-Mayer (Matos 1988b:124) (Figure 4.4).   Figure 4.4. The cosmogram in the Codex Fejérváry-Mayer, folio 1, depicting time and space22 (Museum of the City of Liverpool CC-BY-NC-SA 4.0).                                                   22 "Around a central figure of Xiuhtecuhtli, the lord of the year and of time, the painter arranged the 260 days of the ritual calendar in a multicolored ribbon that defines a Formée cross (often called a Maltese cross). The cross' broad arms are oriented toward the four cardinal directions, with east at the top. Narrower loops between the arms are oriented toward the intercardinal points. The 260 days of the ritual calendar flow along this ribbon in twenty groups of thirteen days, called trecenas. Each trecena is represented by the first day sign of the period followed by the twelve dots that serve as spacers standing in for the other twelve days. Beginning with the first day (Crocodile), the count reads counterclockwise around the cross: the first five trecenas are associated with east and northeast, the second five with north and northwest, the third five with west and southwest, and the fourth five with south and southeast. Each arm of the cross, and thus each direction, has its own color: red in the east, yellow in the north, blue in the west, and green in the south" (Boone 2006b). 130  There were nine subterrestrial levels through which the deceased must pass before reaching the underworld, Mictlan, the "Land of the Dead." These levels were "the Earth, the path through where hills are found, the hill of obsidian, the place of winds formed by obsidian knives, the place where flags wave, the place where people are shot by arrows and where hearts are eaten, the 'Obsidian place of the dead' and the place where no opening exists for smoke to escape" according to the Codex Vaticanus, although Sahagún had a different description of some these levels (Matos 1988b:129).  Furthermore, the geometry of the universe, expressed through the worship of the four directions, is one of the most important ideas of Aztec cosmology. The universe is conceived as the union of four constituent parts of the cosmos in a conceptual pivot through which heaven, the four directions of Earth and the underworld communicate along an axis mundi. Hence, the Aztec space was conceptualized as a vast horizontal disk surrounded by water and intersected by a perpendicular axis conceived as a series of layers, "this disk, sometimes picture as a rectangle, was organize into five major sections (the quincunx), with four quarters" (Aguilar 2007:302) (Figure 4.5).   Figure 4.5. The Aztec concept of space and time (Aguilar 2007:Figure 11.5).  In Aztec cosmology, this cult of the four directions is closely related to the Sun. The Aztecs called this space nauhcampa and it was represented in native codices with east at the top. This is 131  distinct from the European way of representing space with north at this position, which shows the importance of this direction to Aztec society. According to González, each quadrant in nauhcampa was bounded by the solstice points of the rising and setting Sun in its annual journey of 365 days (Figure 4.6). This route had a rectangular plan, whose vertices made it possible to delimit the four quadrants and perhaps where the four holders of heaven were located (1975:51-84).   Figure 4.6. The four quadrants in the universe bounded by solstice points (González 1975:140).  The Aztecs integrated these concepts into architecture and urban design by skewing their sites clockwise from cardinal directions in order to record sunrises in autumn and winter and sunsets in spring and summer (Šprajc 1999b:73). This axial orientation has been confirmed by archaeoastronomers such as Tichy (1974) who found that post- conquest fields, villages and towns were generally aligned east of north. Likewise, Aveni (1975, 1976a), and other scholars have reported that the north-south axes of several pre-Columbian buildings in Central Mexico had a tendency to align slightly east of true north (Figure 4.7). 132   Figure 4.7. Axial orientations of Central Mexican Ceremonial Centres (Aveni and Gibbs 1976: Figure 1).  4.4 The Coordination of Space and Time in the Aztec Calendar  Each of the four cardinal directions ruled 65 days in the Tonalpohualli (ritual calendar), besides influencing each veintena (20 days period); therefore space and time were embedded in the calendar (Aguilar Moreno 302) (Figure 4.8). The origins of this calendar system go back at least as far as the Preclassic period; it was widely utilized among the peoples of Mesoamerica, which is well known through historical and archaeological sources (Pasztory 1983:60).   Figure 4.8. The Aztec Tonalpohualli calendar and the four directions of the world with the Sun in the centre, Codex Tovar, folio 142 (John Carter Library at Brown University CC-BY-NC-SA 4.0).  133  The Aztec calendar system was based on multiple interlocking sets of cycles: • The ritual calendar (Tonalpohualli) •The annual calendar (Xiuhpohualli) • The 52-year calendar round (Xiuhmolpilli)   Figure 4.9. Representation of the Tonalpohualli cycle in which 20 day names interlock with 13 day numbers (Aguilar 2007:Figure 11.1).  The three calendars represented two methods of Aztec time counting. The Tonalpohualli, "counting of the days," was a 260-day cycle, which functioned as a ritual and astronomical calendar used for divination. Its basic units were the trecenas (13-day numbers) and the veintenas (20-day symbols). The 13 day numbers combined with each of the 20-day symbols to generate the 260 days of the tonalpohualli cycle (20 x 13 = 260 days) (Figure 4.9). The Xiuhpohualli, "counting of years," was a 365-solar count that functioned as calendar to organize the recurrent cycle of agriculture and annual seasonal festivals. Under this calendar, the year, xiuhuitl, consisted of 18 "months" of 20 days each plus five additional nemontemi or "leftover" days (18 x 20 = 360 + 5 = 365 days). The combination of the Tonalpohualli and the Xiuhpohualli created a larger cycle of 52 years. The change from one 52-year period, or "bundle of years" (Xiuhmolpilli), into the next was celebrated with the New Fire ceremony, one of the most important religious festivals (Aguilar Moreno 2007:290-298).  134   Figure 4.10. Calendar wheel illustrating the division of the 52-year cycle, Códices Matritenses, folio 188 (Real Biblioteca de Madrid, CC-BY-NC-SA 4.0) .23  The count of 52 years, comprised 73 tonalpohualli (52 x 365 = 73 x 260 = 18980 days) (Figure 4.10). After this period, the combinations of the cycles of 365 and 260 days were exhausted, so another cycle began with exactly the same dates. Two cycles of 52 years, (52 x 2 = 104 years) huehuetiliztli were called "old age" and were further characterized by the coincidence with the cycle of Venus. The Venus year contains 584 days, and five Venus years correspond to eight solar years, so every 65 Venus years coincide with 104 solar years and with 146 tonalpohualli (65 x 584 = 365 = 104 x 146 x 260 = 37960 days) (Broda 2005).  The development of the calendar reflected an astronomical and mathematical knowledge that emerged from the need to adjust agricultural cycles to seasonal cycles. During each month of the solar year, a major festival was celebrated at the temples. The ceremonies of the rain gods and the deities of maize and the Earth constituted a basic calendrical structure, and "it is worth noting that this basic structure of the Aztec ritual calendar coincided closely with the four dates of the year corresponding to the sacred Teotihuacan orientation of 15.5°: April 30, August 13, October 30 and February 12" (Broda 2000:251).                                                  23 The four sets of 13 years are associated with the four cardinal directions, which illustrates the relationship between space and time.  135   This coordination of space and time in the Mesoamerican world (Figure 4.11)was not only expressed in the orientation of architectural structures and urban settlements, but also in the number of days separating the solstitial sunrises and a defined date associated with the beginning of the solar year. These structures are, in most cases, oriented towards the sunrises or sunsets on specific days in the solar cycle, while some of them are also connected with stellar phenomena (Broda 2005).   Figure 4.11. The Boban Calendar Wheel where Aztec architectural building types such as a double temple teocalli and nobility palaces are utilized to describe three main events in the history of Texcoco. These buildings are surrounded by a calendar wheel containing the 20-day glyphs (John Carter Library at Brown University CC-BY-NC-SA 4.0). 24                                                   24 The Boban calendar wheel is the result of a succession dispute between the family of Don Antonio Pimentel Tlahuitoltzin, and Don Carlos Ometochtli Chichimecatecotl, who was backed by Spain. This document was intended to prove that Don Antonio Pimentel Tlahuitoltzin had the legal right to be ruler of Texcoco de Mora. 136  4.5 The Sacred Landscape  It is said that when Cortés described the topography of Central Mexico to Emperor Charles V, he took "a sheet of parchment, crumpled it in his hand," threw it down upon a table and told his monarch that it was like "un papel arrugado" (a crumpled piece of paper). The great mountain ranges running from what is now the Mexican territory are part of the landscape that so impressed the Spaniards. The Trans-Mexican Volcanic Belt (TMVB), that crosses the country from west to east on two primary fractures that cut the terrestrial crust: the Clarion fracture and the Chapala-Acambay fracture, created minor tensional fractures that contributed to the formation of dynamic volcanic system. In the central area of the country, the fracturing of the great volcanoes originated binary volcanic systems such as the Popocatepetl–Iztaccihuatl, the Volcán de Fuego–Nevado de Colima, the Ajusco–Xitle and the Sierra Negra–Pico de Orizaba (Montero 2004:2).  This geographic environment formed a landscape where mountains, caves and rivers established a framework in which daily life was tied to the physical interaction with the environment. The mountains were sacred because they kept a relationship with the sacred.  Broda proposed the concept of sacred landscape for further understanding the orientation of architectural structures and urban settlements, an ideological interpretation of space that connects their geographical space with their cultural space (Broda 1991:74). Time and space converged in the landscape as the annual course of the Sun was tracked on the local topography through a horizon reference system; architecture itself and its coordination with the natural environment were the "writing" (Figure 4.12).  137   Figure 4.12. Horizon calendar of east as viewed from the Templo Mayor (Aveni, Calnek, Hartung 1988:Figure 5).  A system of codes was created within the living landscape. Isolated buildings, architectural assemblages and settlement patterns show particular alignments; in some cases, these alignments were coordinated with specific points of the landscape: mountains or other natural elements like springs and caves, as well as with artificial markers in the form of petroglyphs or buildings constructed deliberately. It is possible there even existed a complex structure of relating the political hierarchies of towns and villages to such an orientation scheme. These points on the horizon, or the orientation of temples to the rising or setting of the Sun and certain stars, were also coordinated with cult practice. The elaborate cult activities were kept in tune with agricultural cycles due to the fact that the basic structure of the festival calendar was the solar year and the main function of ritual was to regulate and control social and economic life (Broda 2000:253-254).  Besides the horizon calendars that tracked the rising or setting of the Sun along the local horizon, the mountain cult was also a fundamental aspect of Aztec cosmovision and religion. According to Sahagún, the Aztecs envisioned the space beneath the Earth filled with water, which came from Tlalocan, the paradise of the god of rain, Tlaloc, and from it issued the springs to form the rivers, the lakes and the sea (Figure 4.13). The purpose of the mountains was to retain the waters as "large vessels or houses full of water and release them when necessary to flood the Earth; that is why they call the villages altepetl which means mountain of water or mountain filled with water" (Broda 1982:49).  138   Figure 4.13. Depiction of Tlaloc in the Codex Borbonicus, folio 5 (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0). 25  The entrances to Tlalocan were the caves, hence they were also considered places of origin, or passages into the womb of the Earth (Figure 4.14 (a)). This conception of space inside the Earth filled with water, and of mountains as containers of that water, is also connected to rains and agriculture, a widespread belief in Mesoamerica (Broda 2000:252). For that reason, the teocallis were built to represent mountains, which were regarded as sources of water and fertility and the dwelling place of their ancestors (Figure 4.14 (b). Mountains were also the symbol of altepetl, "or the heart of the city filled with fertilizing water" (Aguilar 2007:220).                                                   25 In this depiction of Tlaloc, a water stream comes from his body carrying human beings, manifesting the power of water to be destructive as well as generative (Aguilar Moreno 327). 139  Figure 4.14. (a) The caves of Chicomoztoc from which the Aztecs emerged, Historia Tolteca-Chichimeca, folio 16r (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0); (b) Tlaloc seated on his mountain temple, Codex Borbonicus, folio 25 (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0).  4.6 High-Mountain Archaeology  Even though the Aztecs venerated all mountains during the Tepeihuitl (celebration of the mountains) festival, the rituals to Tlaloc (god of rain, lighting and thunder) and Chalchiuhtlicuye (goddess of waters, rivers, and fountains) in other festivities guaranteed the arrival of the rainy season and the regeneration of nature. These rituals were performed in the tetzacualco (mountain shrine) on the summit of Cerro Tlaloc (Figure 4.5), a mountain located in Sierra de Rio Frío  (a)    (b) 140  mountain range on the east of the Valley of Mexico, and is also part of the binary volcanic system with Cerro Telapon (Montero 2004:4). Durán described Cerro Tlaloc as a mountain that was "so tall that clouds always surrounded it, and from it hail, lightning and thunder came out." Since the tetzacualco at Cerro Tlaloc "represented the womb of the Earth as the source of life’s annual renewal" the purpose of these rituals "was to ensure the annual renewal of nature". According to Townsend when the Aztec kings performed the rituals to Tlaloc, they were legitimizing their power by assuring the "renewal of the Earth, the abundance of crops and the order and continuity of society". Besides these rituals in Cerro Tlaloc, other ceremonies were performed on teocallis, fields and other mountains since the Aztecs believed all mountains were related to Tlaloc (Townsend 1992:171-175).    (a) (b) Figure 4.15. Tetzacualco mountain shrine on the summit of Cerro Tlaloc, (a) plan (Iwaniszewski 1994:Figure 3); (b) view towards the east where other mountains and volcanoes can be observed at a distance (Universidad Autónoma del Estado de Mexico 2010:Page 5).  In addition to Cerro Tlaloc, Montero has identified several archaeological remains on eleven important summits in Mexico (Table 4.1). These high mountain sites (4000 meters above sea level) were to the cult of water since pre-classic times and have continued to be a place where contemporary Mexicans perform ceremonies (Montero, 2000:97).  141  Table 4.1. Archeological remains of shrines located on high mountain shrines (Montero 2004)  Name Latitude Longitude Mountain Shrines Elevation Nahuatl Name Ajusco 19.2075 -99.2581 5 sites 3930 Axochco Cofre de Perote 19.4920 -97.1500 3 sites 4220 Naucampatepetl Iztaccihuatl 19.1789 -98.6417 32 sites 5230 Iztaccihuatl Jocotitlan 19.7372 -99.7592 1 sites 3900 Jocotitlan La Malinche 19.2303 -98.0318 22 sites 4430 Matlalcueye Nevado de Toluca 19.1080 -99.7580 18 sites 4690 Chicnauhtecatl Pico de Orizaba 19.0315 -97.2700 15 sites 5610 Citlaltepetl Popocatepetl 19.0230 -98.6220 7 sites 5465 Popocatépetl Volcán Sierra Negra 18.9873 -97.3144 1 sites 4585 Tliltépetl Cerro Tlaloc - Cerro Telapon 19.4123 -98.7126 4 sites- 4125 Tlalocatepetl  Furthermore, the archaeological remains (Figure 4.16) found at these elevations have confirmed their ritual and astronomical function, particularly in regards to their horizon calendars, as solstices, equinoxes and ritual dates could easily be referred to this or that mountain peak. This knowledge was essential to synchronize agricultural cycles with the rainy seasons, the winds, and the cold and warm weather (Montero 2004:25).   Figure 4.16. Register of the archaeological sites found on Volcán Iztaccihuatl (Montero: Figure 2004:75).  142  4.7 Chapter Summary  This chapter demonstrated the multilayered relationship between Aztec architecture and Aztec cosmovision in which the Huey Teocalli was the embodiment of their myths and religious beliefs. It presented the research carried out by archaeologists and historians who have corroborated the myth of Huitzilopochtli with the finding of the Coyolxauhqui stone discovered at the base of the Huey Teocalli along the axis of the temple dedicated to this deity. It also described the concept of the Aztec universe where space was conceived as a vast horizontal disk surrounded by water and intersected by a perpendicular disk organized in four quarters or directions. Each quarter was bounded by the solstice points of the rising and the setting Sun in its annual journey. This solar journey had a rectangular plan whose vertices delimited the four quadrants and where the four holders of heaven were located. Archaeoastronomical research in Central Mexico has established the importance of the space between solstitial points by confirming that post-conquest fields, villages and town have their urban axes skewed towards these directions. Furthermore, this chapter explained how the concepts of space and time were integrated in the Aztec calendar where a complex system of ritual and calendar rounds followed the cycles of the 365-day (73x5=365) Earth year and the 584-day (73x8=584) Venus year in periods of 52 years. This counting of the days was done through horizon calendars where the annual course of the Sun was tracked on the local topography; hence the concept of sacred landscape was introduced. The sacredness of topography was also a fundamental aspect of Aztec cosmovision and religion as the Aztecs envisioned the space beneath the Earth filled with water that emanated from Tlalocan, the paradise of the god of rain. Hence, the religious and cultural importance of Cerro Tlaloc and mountains was presented and explained through the findings of high mountain archaeology.  Consequently, this chapter contributed essential information for the analysis of Aztec architecture and urban planning that was utilized for the archaeoastronomical analyses of the pre-Aztec and Aztec sites selected for this research (Chapter 6), as it established the symbolic importance of the Huey Teocalli of Tenochtitlan, the understanding of the Aztec calendar, the utilization of horizon reference systems and the religious and cultural importance of Cerro Tlaloc. 143  Chapter 5: Aztec Concepts of Astronomy, Mathematics and Geometry  5.1 Introduction  The aim of this chapter is to provide an overview of Aztec astronomy, mathematics and geometry with the purpose of understanding how these disciplines were applied to Aztec architecture and urban planning. This knowledge was necessary to create the horizon reference system to track the Sun at calendrically significant intervals within the solstitial points as presented in Chapter 4 and to construct their cities and buildings. To this end, the first section includes an explanation of archaeoastronomy as well as its foundations and application in the study of archaeological sites; this explanation is followed by an overview of Aztec astronomy; and concludes with a technical explanation about charting the movement of the Sun. The second section introduces Aztec mathematics, including a discussion of numerical systems comprised of linear and angular measuring systems. The third section presents Aztec geometry by demonstrating the embedded design principles within monumental sculpture that were undoubtedly applied to architecture and urban planning. The last section presents an overview of Aztec building practice by describing the roles of the designers and tradesmen, the main construction materials and the construction tools recorded in historical and linguistic sources which conformed a sophisticated design and construction system that was required to lay out their urban centres and architectural structures.  5.2 Archaeoastronomy and Aztec Astronomy  Archaeoastronomy or "cultural astronomy"26 studies the astronomy of ancient cultures. This interdisciplinary area of study requires accurate knowledge of mathematics and astronomy to determine the position of celestial phenomena. Furthermore, it must be based in anthropology, archaeology, ethnohistory, architecture and geography in order to make appropriate interpretations of the orientation of monuments and temples. Even though archaeoastronomy has                                                  26 "The interdisciplinary field of archaeoastronomy has already, by common consent, changed its name into 'astronomy in culture' or 'cultural astronomy.' This happened several years ago although it is still the case that the cultural aspect (cosmovision, or vision of the world) is not always taken sufficiently into account." (Broda 2011:407). 144  its antecedents in the last century, it started to develop as a discipline in the sixties when astronomer Gerald Hawkins hypothesized in his book, Stonehenge Decoded, that the megaliths of southern Great Britain constituted a calendar in stone (Aveni 2001:2).  In Mesoamerica, archaeoastronomy has been a particularly fruitful field of research as ethno- historical records strongly suggest that the positions of, and periods of, celestial bodies were recorded with precision in order to set dates in the ritual and solar calendars (Figure 5.1). The observational elements of pre-Hispanic religion not only included the observation of the annual course of the Sun, certain planets and constellations, but also the observation of geography and natural phenomena in a wider sense.   The detailed observation and accurate prediction of natural phenomena "were intimately fused with a magical attitude and an explanation of the cosmos in mythical terms" (Broda 2001:79). Broda broadens the concept of cosmovision by defining it as "notions about nature and society that were combined into a coherent structural whole and were characterized precisely by this intimate fusion between the exact observation of nature, on one hand, and myth, magic, and ritual on the other" (2001:79). This cosmovision was reflected in their calendrical systems, mathematical calculations, astronomical observations and architecture.   145   Figure 5.1. The Sun god in front of the solar disk, the sky (black band with small circles), the Moon (water-filled vessel with a rabbit), and the Earth (Earth monster below animal sacrificing a quail to the Sun) depicted within a trecena (13-day period) of the Tonalpohualli (260-day ritual calendar), Codex Borgia, folio 51 (Biblioteca Apostolica Vaticana, CC-BY-NC-SA 4.0). 27  The understanding of this cosmovision in architecture and urban planning has been enhanced by archaeoastronomy, as scholars such as Aveni, Hartung, Tichy Galindo and Šprajc, among others, have carried out systematic studies of the orientation of buildings and ceremonial sites, correlated with certain dates of the solar course as they can be observed on the horizon. These reveal that:  "… ancient Mesoamerican time and space were deliberately coordinated in the landscape by means of orientation of buildings and sites, an imposed order that was expressed in the terms of calendrical structure. Ancient Mesoamericans created a sacred landscape in which they tried to establish a harmonious, reciprocal structure among shrines, temples, settlements, and natural features such as mountains and water resources" (Broda 1991:80).  In several cases, the plans of ceremonial centres as well as certain buildings may have been adjusted in order to face a particular direction of astronomical significance (Aveni 2001:259).                                                   27 Interpretation of plate by Nowotny (2005:38). 146  The existence of the Mesoamerican calendar system itself implies astronomical observations maintained through many generations and centuries for its accuracy. Among the observations related to the calendar include the accurate determination of the tropical year, synodic months of the Moon, the cycles of Sun and Moon eclipses, the Venus cycle and the observation of the Pleiades. However, the importance of these phenomena is not evident in the ethno-historical sources; the sixteenth-century chroniclers barely wrote about these aspects of Aztec culture as they did not understand the meaning of the orientations of buildings and urban settlements and their relationship to astronomy. Consequently, in the absence of historical testimony about these aspects of Aztec culture, the archaeological remains have been key to its understanding (Broda 1991:8).  The cosmological relationship between time and space in the Mesoamerican worldview found its expression in architecture by orienting buildings and urban settlements. In most cases, these orientations can be associated with the dates of the rising or setting Sun on specific days of the solar cycle, but some are also related to stellar phenomena. Although several scholars began studying these orientations in particular sites during the early seventies, the decades-long work of Anthony F. Aveni, in collaboration with the architect Horst Hartung, deepened the understanding of these orientations, as they made systematic field measurements with precision instruments of a large number of the Mesoamerican archaeological sites. This data allowed them to make statistical conclusions about the Mesoamerican orientation systems (Broda 1991:9). Their work has been extended by other scholars, including Ivan Šprajc, who studied the astronomical orientations of pre-Hispanic architecture in Central Mexico in 2001.  Another valuable contribution to the study of the orientations was made by geographer Franz Tichy, who developed a specific methodology where he combined the measurement of pyramids and pre-Hispanic sites with the study of the contemporary cultural landscape in Central Mexico. By measuring the orientation of sixteenth-century churches, he was able to determine the dominant orientation system in this cultural area (Tichy 1988a:117).  The interest in the study of orientations of archaeological sites lies in the fact that the orientations represent a calendrical principle different from those represented in stelae and codices. This is 147  certainly a principle unfamiliar to Western thought, as the "writing" is architecture and its relationship with the natural environment: A code system is reflected in the landscape. In many cases, individual architectural elements, urban assemblages and whole settlements reveal some specific orientations. These sites, in turn, are related to specific points on the topographical landscape with mountains and other natural or artificial markers (Broda 1992:37).  5.2.1 Aztec Astronomy  Similar to other Mesoamerican cultures, astronomy had a prominent role in Aztec culture (Figure 5.2). Several pictorial manuscripts relate historical events with natural phenomena such as eclipses, meteor showers, comets and the aurora borealis. However, Aztec astronomers were mostly interested in following those celestial bodies whose cyclical movements were supposedly connected to the Sun (Aguilar 2007:304).   Figure 5.2. Aztec astronomers observing the sky (represented a black semi-sphere with small white and red eyes), Codex Mendoza, folio 63 (Bodleian Library, CC-BY-NC-SA 4.0).  The annual movement of the Sun was followed closely by astronomers who recorded solstices, equinoxes and zenith passage; these dates marked the ceremonies that were related to agricultural cycles and other important dates. The Sun is extensively depicted in both anthropomorphic and symbolic manner in pictorial manuscripts and associated with numerous rites, ceremonies and temples. It is also connected to the creation myth and the birth of 148  Huitzilopochtli, so it was revered every day and within different ceremonies (González 1975:51-83).  In the Florentine Codex, Book II: The Ceremonies, Sahagún describes in detail the elaborate festivals during each of the 18 months of the annual calendar or Xiuhpohualli, thus implying that priests followed with precision the movement of the Sun. Each festival was celebrated in the last day of the month, although some preparatory ceremonies started 20, 40, or 80 days before the main festival; and others lasted 20 or 40 days after the main festival (Figure 5.3).    Figure 5.3. The Atamalqualiztli Festival which was celebrated every eight years; during this time they only ate tamales made with water and salt, Primeros Memoriales, folio 254r (Real Biblioteca de Madrid, CC-BY-NC-SA 4.0).  Furthermore, in the Florentine Codex, Book VII: The Sun, Moon and Stars, and the Binding of the Years, Sahagún narrates, among other stories, the Legend of the Fifth Sun—the fifth era of a cycle or creation and destruction—and the rites during the annual Sun festival. Broda and Aveni have documented that the Atlcahualo ritual ceremonies dedicated to Tlaloc, the rain god, took 149  place in a diverse set of ceremonial landscapes which involved the sacrifice of many children on shrines in several mountaintops around Lake Texcoco (Aveni 1991:58).  The cycle of birth, growth, plenitude and decline of the Moon was also recorded by the astronomers, who associated it other natural phenomena with similar cycles such as plants, menstruation, fertility and reproduction. It was also represented in the codices and associated with the creation myth and the birth of Huitzilopochtli, as the disremembered body of Coyolxauhqui. Historical sources do not mention any ceremony or temple directly related to the Moon, however there were lunar rituals associated with other ceremonies (González 1975:51-83). For example, Sahagún describes how a pregnant woman placed a piece of maguey in her bosom in order that the child would not be born deformed during lunar eclipses (Figure 5.4).   Figure 5.4. Eclipses of Moon and Sun, Primeros Memoriales, folio 282r (Biblioteca Medicea Laurenziana, Firenze, CC-BY-NC-SA 4.0).  After the Sun and the Moon, Venus is the brightest star in the sky, so Aztec astronomers also followed its synodic periods. Venus is depicted in both anthropomorphic and symbolic manner in pictorial manuscripts. Its aspects, Morning Star and Evening Star, were worshipped by the Aztecs (González 1975:103-107). Furthermore, they associated Venus with the god who guided the dead to the underworld (1975:117) since it is not visible for about 58 days when it is behind the Sun (50 days) or in front of the Sun (eight days). 150   Because of its synodic period of 584 days, it aided astronomers in the calibration of their calendar of 365 days. Five Venus cycles (5x584=2920), correspond to eight Earth cycles (8x365=2920) in a precise 8:5 ratio, so 65 Venus cycles were the equivalent of 104 Earth cycles. This 104-year cycle was called the Huehueliztli, which means "very long age." This cycle is also related to the calendar, because it was divided in two Xiuhmolpilli of 52 years, which were celebrated with a New Fire ceremony (Aveni 2001:148). However, the main importance of Venus was in soothsaying despite having a temple and ceremonies associated with it.  Celestial bodies and constellations were also venerated because many of the star groups had associated gods (Figure 5.5). One of the most astounding aspects of the Florentine Codex, Book VII: The Sun, Moon and Stars, and the Binding of the Years is that it gives a pictorial and written account of certain constellations by "representing the stars as circles connected by lines, which is reminiscent of the constellation patterns which can be seen inscribed around the periphery of the Aztec calendar stone" (Aveni 2001:32).    Figure 5.5. Aztec constellations, left (from top to bottom) Mamalhuaztli, Tianquiztli, Citlaltlachtli; right (from top to bottom Citlalxonecuilli, Citlalcolotl, Primeros Memoriales, folios 282 r y 282v (Biblioteca Medicea Laurenziana, Firenze, CC-BY-NC-SA 4.0).  Since astronomers needed to determine certain points on the horizon, pictographic evidence suggests that Mesoamerican astronomers utilized a pair of crossed-sticks as sighting devices (Figure 5.6). An astronomer could plot the position of an object near the horizon with precision by utilizing one crossed stick as a foresight and the other as a backsight. Even a distant point in 151  the landscape, such as mountain or a structure, could function as a foresight (Aveni 2001:65). This method could be used to calculate the synodical revolution of a celestial body as the astronomer only needed to count the days until it returned to its recorded position (Aguilar 2007:306).    (a) (b) Figure 5.6. (a) Astronomer using a pair of crossed-sticks set up on top of a temple to determine a position of a celestial body; (b) An arrangement of two crossed-sticks through which an astronomer views a V-shaped arrangement in the distance, where a celestial body, probably the Sun, can be seen, Codex Bodley, plate 15 (Bodleian Library, CC-BY-NC-SA 4.0).  This astronomical knowledge, particularly the charting of the Sun, was used by the Aztec to lay out cities and buildings because ceremonial centres served as focal points in rituals. Aveni, Calnek and Hartung have thoroughly investigated the ethno-historical arguments about the orientation of the Tenochtitlan and found several circumstantial reasons for postulating an intentional astronomical orientation. One of the most compelling arguments is described by Motolinía who recounts how the Templo Mayor had to be rebuilt because it did not align with the equinox:  Tlacaxipehualiztli. On this day they flayed all of the enemy prisoners, and dressed themselves in their skins; and they dedicated this festival to Tlatlauhqui Tezcatlipoca… This festival fell when the Sun was in the middle of [the temple of] Huitzilopochtli, which was the equinox, and because this was a little twisted Moctezuma wished it torn down and straightened (Aveni, Calnek and Hartung 1988:290). 152   Taking into account Motolinía's statement, Maudslay hypothesized that "the priest and worshippers doubtless faced to the east, to watch the Sun rise in the space between the two oratories." Maudslay's idea was further reinforced by a 1524 map of Tenochtitlan which shows a face representing the Sun flanked by twin temples on the top of the Templo Mayor (Aveni and Gibbs 1975:513) (Figure 5.7).   Figure 5.7. Ceremonial precinct depicted on the Map of Tenochtitlan included in the Second Letter of Cortes published printed in celebriciuitate Norimberga [Nuremberg] in 1524. Even though the ceremonial centre was rotated -90° from its real orientation, the face of the Sun is depicted as an animate being seen emerging between the twin temples of the Huey Teocalli (Newberry Library, Chicago, CC-BY-NC-SA 4.0).  Apparently, the archaeological record indicated that the Templo Mayor deviated 97.5° east of north, which indicated apparent conflict between historical and archaeological evidence. However, they concluded that this deviation was necessary because the Sun moved toward the southeast on a slanted path to an altitude of about 22 degrees above the astronomical horizon before it could effectively be seen between the temples during the equinox (Figure 5.8).  153   Figure 5.8. Orienting of a temple towards the Sun on the horizon and adjusting an orientation of Sun at horizon to Sun over temple (Aveni, Calnek and Hartung 1988:Figure1).  Other scholars, such as Sejourné, refute this theory and affirm that this orientation corresponded to the zenith passage, while Aveni and Hartung believe that orientation phenomena are the product of a tradition that began in Teotihuacan where the "equinox sunset is marked by a line passing from the top of the Pyramid of the Sun through a pair of petroglyphs at ranges of 6.5 and 7.5 km respectively that lie on the horizon precisely in line with the pyramid and at approximately the same elevation as its summit" (Aveni, Calnek and Hartung 1988:307).  In conclusion, no single explanation has been offered to explain the orientations of all known Aztec buildings and urban settlements in spite of the ubiquitous presence of these solar alignments in post-conquest churches, plazas and surrounding areas. This has led Tichy to posit the existence of three groups of axial orientations: a group near 7 degrees, a group near 17 degrees, and a group near 26 degrees east of north. This confirms a deliberate effort to orient Aztec buildings and urban settlements in these directions.  154  5.2.2 Charting the Movement of the Sun  Since the most important dates of the solar cycle—solstices, equinoxes and the path of the Sun through the zenith—were the most clearly expressed in architecture in Central Mexico (Šprajc 2001:411), a scientific understanding of orientations and the charting of the movement of the Sun is pertinent.  Figure 5.9. (a) The annual path of Earth around the Sun. (b) The tilt of the Earth's axis in the plane of the ecliptic results in the seasonal variations (Stein, et al. 2006:150).  The most obvious of the celestial motions is the path of the Earth around the Sun. Viewed from Earth, this trajectory has two directions: north-south and east-west. The east-west direction is indicated by the daily movement of the Sun across the sky; every day the Sun appears in the east and sets in the west. The Sun also moves annually for six months from north to south, then for the remaining six months of the year, from south to north. This north-south-north annual movement is easily visible on the horizon as the sunrise-point (orto) appears slightly offset from the point of departure the previous day. This apparent path of the Sun on the horizon has two extremes: around June21st on the Summer Solstice in the Northern Hemisphere when the Sun 155  reaches the peak on its way north, and around December 21st, on the Winter Solstice in the Northern Hemisphere when the Sun reaches its farthest point in its journey south (Figure 5.9). The apparent motion of the Sun on the horizon is due to the tilt between the axis of rotation of the Earth and the plane of the ecliptic (Aveni 2001:49-55).   Figure 5.10. (a) The position of the Sun is expressed in terms of the vertical angle above the horizon (altitude) and the horizontal angle (azimuth). (b) Approximate position of the Sun in each of the seasons at a mid-northern latitude. Note that the altitude angle is maximum in the summer, minimum in the winter, and in between in spring and fall (Stein, et al. 2006:151).  The ecliptic is the apparent path of the Sun across the sky. The axis of rotation of the Earth forms, with the perpendicular to the plane of the ecliptic, an angle of 23.5 °. As a result of that inclination, during the Summer Solstice in the Northern Hemisphere, solar rays fall perpendicular to the Tropic of Cancer, located at 23.5 ° North of Equator. Conversely, during the Winter Solstice in the Northern Hemisphere, Sun rays fall perpendicular on the Tropic of Capricorn, located at 23.5 ° South of Equator. This variation in the inclination of the solar rays on the surface of the Earth causes the cyclic changes of season (Aveni 2001:55-58) (Figure 5.10). 156   Figure 5.11. (a) The sky vault is represented as a hemisphere, which projects as a circle (b) on a projection plane. The exact shape of the Sun path chart depends upon the projection method. The hour points of the Sun path chart are connected to form hour lines that are useful for interpolation (Stein, et al. 2006:154).  Since there is historical and archaeological evidence that certain dates were considered in urban and architectural planning, charting the movement of the Sun during solstices, equinoxes and zenith passages is part of the study of Aztec architecture (Figure 5.11 This can be achieved through the utilization of Sun path calculations, Sun path charts (Figure 5.12) and topographical maps. 157   Figure 5.12. Equidistant (horizontal, polar) Sun path diagram for 44 degrees latitude (Stein, et al. 2006:156).  5.3 Aztec Mathematics  Ethno-historical records reveal that the Aztecs devised complex numerical systems that were not only utilized for calendrical and economic purposes (Payne and Closs 1986:214), but also for recording measurements and calculating the areas of houses, fields and streets (Harvey and Williams 1980:499; Williams and Jorge 2008:72). These systems used both picture symbols and lines and dots for numerical notation, incorporated a symbol for zero and used position to ascribe values.  158   Figure 5.13. Aztec numerals(a) 1; (b) 20; (c) 400; (d) 8000 (Closs 2008:Figure1).  As elsewhere in Mesoamerica, the Aztec numerical system was base 20, cem-poalli, literally translated "one count." The next place in the system is or  400 (cen-tzontli), literally translated "one hairs." The largest place denoted by a special term is  or 8000 (ce-xiquipilli), literally "one bag." (Harvey and Williams 1980:499) (Figure 5.13).   Figure 5.14. Contexts of Aztec numeral usage. Calendar dates: (a) 13 Rabbit; (b) 8 Reed. Chronological counts: (c) 70 years; (d) 5206 years. Tribute records: (e) 100 copper hatchets; (f) 1200 coarse clay pots; (g)   8000 balls of unrefined copal wrapped in palm leaves (Closs 2008:Figure2).  The integers between places are quantities to be added or multiplied. Thus, integers from 1 to 19 were represented by the appropriate number of dots or circles. The numeral 1 was represented by a single dot or a finger; 2, 3, and 4 were represented by two, three, and four dots, respectively; 5 159  was represented by five dots or a full bar; 6 through 9, by dots alone or a combination of dots and a bar; 10 was represented by ten dots, two bars or a rhombus. The integers between 10 and 20 were represented as a combination of dots, bars and a rhombus.   Figure 5.15. Tributes of Tlaxinican, Tlaylotlacan, Tecpanpa, etc. depicting number—represented by symbols on above objects—coins, fish, and waterfowl paid as tribute to Colonial authorities (Archivo General de la Nación de México ,CC-BY-NC-SA 4.0).  Similarly, multiples of 20 but less than 400 were represented by repeating the symbol of 20 as many times as necessary; integers between 400 and 8000 were repeated to form multiples of 400 and multiples of 8000 respectively (Closs 1368). This progression continued until the number 64000000 (8000 x 8000), a sufficient count to respond to the needs of the Aztec (Figure 5.14). The order of the terms followed a rigorous, logical and scientific progression which enabled them to compute large sums, especially when they were dealing with matters involving tribute pay (Aguilar 2007:314) (Figure 5.15).  Aztec numerals are found in several contexts, most commonly as coefficients in calendar dates, chronological counts and tribute records that consisted of lists in which the quantities of the various tribute items to be received from conquered towns were recorded (Closs 2008:1369). However, these numerals were found during the course of this research in several land titles and administrative documents as illustrated in Figure 5.16. 160    Figure 5.16. Plan and title of a property in Huexocolco, depicting measurements—represented by dots around the perimeter—of house and chinampas (Archivo General de la Nación de México ,CC-BY-NC-SA 4.0).  5.3.1 Linear Measuring System  In addition to picture-symbols, Aztecs used a positional line-and-dot system for recording the measurements of perimeters and areas of land holdings in at least two locations in the Valley of Mexico in Tepetlaoztoc. This system, contained in the Codex Santa Mara Asunción and the codex Vergara, employed only three symbols that were easy to draw: a vertical line, a bundle of five lines linked at the top and a corn glyph (cintli) with position indicating the value of the symbols (Figure 5.17). Harvey and Williams have noted that this system would seem to be more applicable and well-suited in general for arithmetic calculations (Harvey and Williams 1980:99).  161   Figure 5.17. A land record from the codex Santa María Asunción (Harvey and Williams 1980:Figure 1).  Williams and Jorge revised the algorithms present in 408 quadrilateral fields of all five Codex Vergara localities and discovered "evidence for the use of congruence principles, based on proportions between the standard linear Acolhua measure and their units of shorter length" (Figure 5.18). This procedure substitutes for computation with fractions and is labeled "Acolhua congruence arithmetic." The findings also clarify variance between Acolhua and Tenochca linear units, long an issue in understanding Aztec metrology (Williams and Jorge 2008:72). An example of the application of these fractional units can be seen in the plan of the House of Ana Justina, San Hipólito Teocatilan District, where the measurements of the property are represented by hands, hearts and arrows glyphs (Figure 5.19).  162   Figure 5.18. Acolhua equivalences inferred from computation of Acolhua recorded areas. The hand, heart and arrow are referents for proportions 5:3, 5:2 and 2; the bone and arm are tentatively proposed glyphic referents for proportions 5:1 and 3:1 (Williams and Jorge 2008:Figure 2).   Figure 5.19. Measurements of property in hands, hearts and arrows, House of Ana Justina, San Hipólito Teocatilan District, 1593 (Archivo General de la Nación de México ,CC-BY-NC-SA 4.0).  In 2010, Clark refined and tested Aztec linear measurements in two Aztec palaces and applied them to the ceremonial precinct of Tenochtitlan. Similar to Sugiyama in Teotihuacan, he found 163  that the precinct was built according to the dimensions of sacred time that utilized Aztec linear measurement units. Based on research done by Castillo (1972), Molina (1977) and Williams and Harvey (1997), Clark affirms that Aztec linear measurements were calibrated to the human body (Figure 5.20). This is similar to the Spanish system as both utilized various arm measures.   Figure 5.20. Aztec units of measure and their body referents (Clark 2010:Figure 12.1).  The maitl (hand) was the measure between the outstretched hands, the yollotli (heart) the measure from the centre of the chest to an outstretched hand. Utilizing the Aztec units, and correlating them to Spanish linear units (83.5905, the Castilian vara of Burgos), Clark developed a series of equivalencies between Aztec linear measures and their metric values (Figure 5.21).  164   Figure 5.21. Aztec linear measures and their metric values (Clark 2010:Table12.1).  An example of the utilization of different units for quantities (probably referring to the number of descendants as this document is a genealogy according to Elías Caracas) and for linear measurements indicating the perimeter of the house can be found the Títulos de Propiedad de Mexico-Tenochtitlan (Property titles of Mexico-Tenochtitlan) (Figure 5.22). 165   Figure 5.22. Property titles of Tenochtitlan utilizing two types of numeral, one for quantities (blue flag and dots on top) and measurements of house in hands, dots and arrows (Archivo General de la Nación de México, CC-BY-NC-SA 4.0).  5.3.2 Angular Measuring System  Tichy postulated an angular measurement unit that resulted from the statistical treatment of directional values in the basins of Central Mexico. He surveyed the axial directions of almost 300 churches, the colonial successors of the temples, and found that they were concentrated around astronomical east-to-south with the clockwise deviation 1-2, 11-12, 16, 20 and 25 degrees (Tichy 1988:106) (Figure 5.23).  166   Figure 5.23. Diagram of the Mesoamerican Orientation System. The alignments are in accordance with the hypothetical solar orientation calendar with 13-day weeks. The clockwise deviations from east represent the "winter sunrise Maya type" and the deviations from West, the "Summer Sunset Central Mexico Type" (Tichy 1988:Figure7).  The correlation with the movement of the Sun can be observed in the direction of the solstice (25 degrees), the directions of the sunset on the days of the passage of the Sun through the zenith on 19 degrees N.L., and the midyear days near the equinoxes (1 degree). The 1, 7 and 16 degrees directions are explained by the first days of the periods of 20 days in a hypothetical fixed Sun calendar according to the description of Sahagún for 1564-67. According to Tichy, the basis of these orientations was not simply the calendar, but also a geometric system that consisted of arithmetical angular series with 4.5 degrees intervals (Tichy 1988a:107).  Tichy suggests that this angular measure was taken from the human body, as it was possible to indicate a distance on the horizon using the extended arm with spread fingers (Figure 5.24). With the width of five spread hands, one can cover a right angle, about 18 degrees per hand. In this way, with the outstretched arm, the horizon can be measured with a quarter of an open palm or a twentieth of the right angle, 4.5 degrees (Tichy 1988:106). 167   Figure 5.24. Reconstruction of an astronomical device based on an illustration in the Codex Selden that was probably used throughout Mesoamerica. It is the size of a hand with spread fingers and made of a bundle of twigs. When the hand is outstretched, the angle between the two tips, which are 4.3 cm apart, is 4.5 degrees or 1/20th of a right angle (Tichy 1988:Figure 9).  5.4 Aztec Geometry  The first attempt to study Aztec geometry in monumental sculpture was performed by Antonio León in Gama in 1792 when he utilized geometrical figures and measurements to analyze the Coatlicue and Aztec Sun Stone in his essay, A Historical and Chronological Description of Two Stones which were found in 1790 in the Principal Square of Mexico During the Current Paving Project (León y Gama 2010:65-76). More than a century later, in 1928 Alfonso Caso tried to investigate the module or unit that was utilized in its construction by measuring the Sun Stone, the Tizoc Stone, and the Quetzalcoatl temple in Xochicalco, and found several geometrical relationships among them. In 1953, Raúl Noriega analyzed the mathematical aspects of the Sun Stone and fifteen other solar monuments. These mathematical studies were continued in 1992 by Oliverio Sanchez, who deduced the construction methods of the geometric figures and the mathematic relationships embedded in the geometry of the Aztec Sun Stone (Ramirez 1995:50-56) (Figure 5.25). In 1995, Ramírez Bautista applied these methods in his analysis of the Sun Stone, the Stone of Tizoc and the Ex-archbishopric's Palace Stone, concluding that the presence of these geometrical principles among solar monuments demonstrated the existence of Aztec geometry (Ramírez 1995:108). 168    Figure 5.25. The geometric composition deduced by Oliverio Sánchez based in two interrelated pentagons (Ramirez 1995:Figure 16).  In 1996, Rivera applied geometrical and achaeoastronomical principles to the analysis of Aztec architecture. She demonstrated that both the Templo Mayor and the ceremonial precinct of Tenochtitlan had an embedded underlying geometry within their design. Later, in 2000, Martínez, analyzed several examples of Mesoamerican sculpture and architecture utilizing a more systematic geometric approach (Figure 5.26).   Figure 5.26. Geometric study of the Coatlicue (Martínez 2004:Figure 5.44).  169  In an urban scale, Sugiyama applied a geometric analysis methodology in his measurement study of Teotihuacan in the 2000s. He not only found direct relationships between the base ratios of the pyramids with the ritual and the solar calendars, but also inferred the measurement unit (Teotihuacan Measurement Unit, TMU=83.0 cm.) that was employed to build the city and its temples (Sugiyama 2010:134) (Figure 5.27).   Figure 5.27. Plan of Teotihuacan with possible measured distances indicated in TMU (Sugiyama 2010:Figure 11.3).  Ramírez (1995), Rivera (1996) and Martinez (2010) have demonstrated that Aztec sculpture and architecture utilized several geometric figures either directly on their designs or underlying as regulating lines within their designs. These figures include: circles, triangles, squares, rectangles and several polygons.  170  5.4.1 Geometric Figures in Aztec Design  5.4.1.1 Circle  The circle, defined as "a plane curve consisting of all points at a given distance called the radius from a fixed point called the centre," is the geometric figure that contains all the possible regular polygons. It is a figure that does not have a beginning or an end, and with an infinite number of sides, it has been considered a symbol of unity, infinity and divinity in many cultures (Calter 2008:168). Its diameter, which corresponds to the diagonal of the maximum square that can be inscribed into the circle, represents the first division of the unit. Furthermore, the relationship between the circumference (the total length of the circle) and its diameter, generates one of the most important mathematical constants, Pi (π):   In Aztec culture, the circle represented a cycle as well as a unit in written numerals (Payne and Closs 1986:228). The circle was associated with the Sun, the Moon, Tlaloc and Aztlan, also called Cemanahuac, the place in a circle of water which was also in the middle of a lake (Figure 5.28). The Aztecs symbolically referred to the Valley of Mexico, and in general to the world, as Cemanahuac or Anahuac (Aguilar 2007:230).  171   Figure 5.28. Schematic representation of the Aztec worldview (Matos 1988:Figure 107).  5.4.1.2 Polygons  A polygon defined as a "plane figure bounded by straight-line segments which are called the sides which intersect at points called the vertices," can be primarily classified by the number of sides. Ramírez meticulously identified several underlying polygons — including pentagons (5 sides), hexagons (6 sides), heptagons (7 sides), octagons (8 sides), nonagons (9 sides), hendecagons (11 sides), tridecagons (13 sides), pentadecagons (15 sides) and heptadecagons — on the Aztec Sun Stone, the Tizoc Stone and the ex-Archbishopric's Palace stone that required an advanced knowledge of geometry (Ramirez 1995:87-100) (Figure 5.29). 172   Figure 5.29. Underlying polygons in the Aztec Sun stone (Ramírez 1995:Figure 29).  5.4.1.3 Triangles  The triangle or trigon, defined as a "polygon with three vertices and three sides" (Calter 2008:67), is an integral part of the design in Aztec solar monuments. Isosceles triangles are always placed in on equidistant points along the main circle and an underlying octagon. Superimposed equilateral triangles are circumscribed within the circle to form the four segments of the ollin symbol on the Aztec Sun Stone (Ramírez 1995:96) (Figure 5.30).  173   Figure 5.30. Superimposed isosceles triangles in the Tizoc Stone (Ramírez 1995: 95).  5.4.1.4 Square and Rectangles  The square defined as a "polygon with four equal right angles (90°) and four equal sides," derives directly from the circle when two of its perpendicular diameters turn into diagonals of the maximum square that can be inscribed within it. An infinite number of rectangles can be derived by the diagonal of the square, producing a root rectangle, defined as a rectangle with an irrational number as the ratio of length to width: , , , … (Calter 2008:98). Even though squares are present within the underlying geometries of Aztec solar monuments, Martínez argues that the most common figure utilized in architecture was the rectangle, that she has named the Σ rectangle 7x8 (2000:26-56).  174   Figure 5.31. Σ rectangle 7 x 8 (Martinez 2000:Figures 2.6 and 2.7).  She defines a Σ rectangle as a square in which a unit has been added (or removed) to its two parallel sides, which is to say that the difference between a square and the Σ rectangle is another rectangle that has the unit as its base and the height of the square. The resulting rectangle is a unit-rectangle. Consequently, the design unit of the Σ rectangle is the difference between the lengths of its sides (Figure 5.31).  Martínez and Sugiyama have found the Σ rectangle in three pyramids in Teotihuacan (Sugiyama 2010:133) (Figure 5.32), Chichen Itzá and in the trapezoidal base represented on the first page of Codex Fejérváry Mayer.  175   Figure 5.32. Plan of the Sun Pyramid complex with the Avenue of the Dead with measurements in meters and TMU (Sugiyama 2010:Figure 11.5).  In architecture, some architectural aspects and sculptural panels of pre-Columbian structures (particularly Mayan), were analyzed by Manuel Amábilis in 1929 (Figure 5.33). Despite the interest that his work aroused at that time, it is possible that his research was not widely publicized due to his strained relationship with Ignacio Marquina after Amábilis won the Gold Medal in the contest of the Royal Academy of Fine Arts of San Fernando in Madrid, in which Marquina had also participated with his work Estudio Arquitectónico Comparativo de los Monumentos Arqueológicos de México.  176    (a) (b) Figure 5.33. (a) Stone panel on wall of the Monjas complex at Chichen Itza, (b) Geometric analysis of panel (Amábilis 1956:Figure 75).  Even though this mathematical and geometrical knowledge is not recorded in historical sources, its presence is evident in sculpture and architecture. Considering that it would not have been possible to sculpt precise designs on the Aztec Sun stone as Ramírez has demonstrated or layout Teotihuacan, a city of 125 000 people, as Sugiyama has discovered, without applying mathematics and geometry, it can be suggested that the Aztecs must have utilized this knowledge in architecture and urban planning   In 1996, Rivera examined the ceremonial precinct of Tenochtitlan utilizing geometrical in conjunction with achaeoastronomical principles from an architectural point of view. Her studies revealed an underlying geometry that established relationships of the main buildings and secondary precincts with the Great Temple (Figure 5.34).  177   (a)   (b) Figure 5.34. Digital interpretation of the ceremonial precinct of Tenochtitlan based on the geometric and archaeoastronomical analyses performed in the urban arrangement and each architectural type; (a) regulating lines of the Huey Teocalli; (b) digital interpretation with structures found in both ethno-historical sources and archaeological records (Rivera 1996). 178   After Rivera, Martínez has been the only scholar to address Mesoamerican geometry. However, Sobral has mostly concentrated on small scale sculpture and two buildings: the pyramid of the Sun in Teotihuacan and the Castillo in Chichen Itzá. Coupled with this, architectural design research is an emerging research field that began to be recognized in 1996 when Mario Salvadori presented his paper "Can There be any Relationships Between Architecture and Mathematics?" at the Nexus-Architecture and Mathematics conference in Fuceccio, Italy (Salvadori 1996:10).  Furthermore, the inclusion in these analyses of Mesoamerican measurement systems has only been explored by Rivera in the Huey Teocalli (1996), by Sugiyama in Teotihuacan (2005, 2010), and by Clark in the Oztoticpac palace and the precinct of Tenochtitlan (2010). These scholars have just opened a field of study within architectural design and archaeology that promises to be quite fertile due to the rich Mesoamerican built heritage.  5.5 Aztec Building Practice  In addition to possessing sophisticated astronomical, mathematical and geometric knowledge to layout urban centres and architectural forms, the Aztecs also had a complex building practice that involved highly skilled craftsmen, construction materials and specialized tools. These craftsmen were organized in calpulli, a basic structural unit of Aztec society composed of a group of commoners (usually kin groups) who held land in common and were also dedicated to the same socio-economic activity such as farming, practicing the same craft and trading (León Portilla 137). Each calpulli had a Telpochcalli, where sons of commoners were taught religion, military skills and a craft or trade, while sons of the nobility attended the Calmecac, where priests taught them religion, mythology, history, calendrics, writing, engineering and law, along with thorough military training (Figure 5.35). Students educated and disciplined in the calmecac were competent to fill leadership and important public posts (López Austin and López Lujan 2001:221-223).  179     (a) (b) (c) Figure 5.35. (a) A calpulli, (b) Parents delivering their sons to the Calmecac, (c) Calmecac priest addressing students, Florentine Codex, Books 2, 3, and 2 respectively (Biblioteca Medicea Laurenziana, Firenze, CC-BY-NC-SA 4.0).  Even though there is no direct mention in historical sources of a calpulli of builders, Sahagún describes several building types (Figure 5.36) as well as trades related to building practice such as carpenters, stonemasons and plasterers. These trades undoubtedly worked with painters and sculptors as architectural expression and sculptural work were related in their formal and spatial expression in many cultures throughout Mesoamerica, including Aztec.  This relationship between the Aztec architecture and cosmovision was reaffirmed in 1978 when the Coyolxauhqui stone was discovered accidentally while a group of workers opened a trench to place wires in the center of Mexico City. Matos recounts, "… from the moment when the sculpture was fully excavated, we realized that it was a dismembered female figure that could only match the Coyolxauhqui. This raised the possibility of finding what for nearly 200 years we had eagerly sought from the time that Coatlicue, mother of the gods, was discovered in 1790… the Great Temple of Tenochtitlan" (Matos 1981:106-107). This discovery marked a new era of Aztec scholarship and provided a fertile area for Aztec architectural research.  The Coyolxauhqui stone, snake heads attached to the balustrades of the stairs, and other sculptures found in several building stages of the Templo Mayor, strengthened the relationship between sculpture and architecture. Furthermore, the overall construction of the buildings excavated in the site, the foundations, vestiges of floors and other engineering and architectural details revealed how different trades like carpenters, stonemasons, bricklayers and painters had 180  to work together with "wise men" [architects and engineers] to build the ceremonial precinct of Tenochtitlan.   Figure 5.36. "De los diferentes edificios" ("About the different buildings"); a double teocalli depicted on the left, and a tradesman building the teocalli on the right, Florentine Codex, folios 240r and 241v (Biblioteca Medicea Laurenziana, Firenze, CC-BY-NC-SA 4.0).  181  5.5.1 Construction Trades and Architect  In Chapter 8, Book 10, "About other skilled workers such as carpenters and masons," Sahagún gave a detailed description of these trades, which are illustrated in some cases:  Carpenter 28 The carpenter, his job is to do the following: cutting with ax, splitting beams, making pieces; sawing, cutting branches of trees, and splitting pieces from any tree. The good carpenter usually measures wood and lays it with a level; and adjusts it with the joiner so that it goes straight; he levels, matches, matches, fits it with other pieces, and put the beams in order across the walls; in short, he is skilled in his craft. The bad carpenter ruins what is right, and is neglectful, a cheat and damages the work he is given to do, and in everything he does, he is awkward and careless (Figure 5.37).   Figure 5.37. The carpenter, Florentine Codex, Book 10, folio 17r (Biblioteca Medicea Laurenziana, Firenze, CC-BY-NC-SA 4.0).                                                   28 Carpintero  El carpintero, es de su oficio hacer lo siguiente cortar con hacha, hender las vigas, y hacer trozos, y aserrar, cortar ramos de árboles, y hender concuñas cualquiera madero. El buen carpintero suele medir, y compasar la madera con nivel, y labrarla con la juntera para que vaya derecha, acepillar, emparejar, entarugar, encajar unas tablas con otras, y poner las vigas en concierto sobre las paredes, al fin ser diestro en su oficio. El mal carpintero desparpaja lo que está bien acepillado, y es descuida-do, tramposo y dañador de la obra que le dan para hacer, y en todo lo que él hace es torpe, y nada curioso. Translated by Rivera.  182  Stonemason 29 The stonemason has strength, is vigorous, lightweight and clever, carving and shaping any stone. The good mason is a skilled worker, knowledgeable, proficient working the stone, adjusting corners; and splitting with wedge; making arches; sculpting; and carving the stone in great detail. It is also his job to trace a house;, make a good foundation; add corners; make roofs; well-made windows and partitions. The bad stonemason; is lazy; carves poorly; and does not let the walls harden; makes them crooked; and laying on a side and bulging (Figure 5.38 (a)).    (a) (b) Figure 5.38. (a) Several activities performed by stonemasons, Florentine Codex, folio 20v; (b) Mason and assistant preparing sand for plaster, folio 20r (Biblioteca Medicea Laurenziana, Firenze, CC-BY-NC-SA 4.0).                                                   29 Cantero  El cantero tiene fuerzas, es recio, ligero y diestro en labrar y aderezar cualquiera piedra. El buen cantero es buen oficial, entendido, hábil en labrar la piedra, en desbastar, esquinar, y hender con la cuña, hacer arcos, esculpir, y labrar la piedra artificiosamente. También es su oficio trazar una casa, hacer buenos cimientos, poner esquinas, hacer portadas, y ventanas bien hechas, y poner tabiques en su lugar. El mal cantero, es flojo, labra mal, y en el hacer de las paredes no las fragua: las hace torcidas, y acostadas a una parte, y corcovadas. Translated by Rivera.  183  Mason 30 The work of the mason is making mixture well and plastering surfaces with lime; leveling and polishing them well. The bad craftsman is clumsy; his whitewash is reckless, not smooth; but with holes, rough and uneven (Figure 5.38 (b)).  Painter 31 The work of the painter is using his craft to know colors and draw, or making drawings with coal; and making very good mix of colors; and knowing how to grind and mix them well. The good painter has good hand and grace in painting; and thinks about what he has to paint; mixes and blends the paint well; and knows how to make shadows and foliage. The bad painter has a wicked and silly wit; which makes him annoying; and does not fulfill the expectations of those who give him the work, does not give luster to his paintings, is confusing, disorganized and without proportion and done in a hurry (Figure 5.39).   Figure 5.39. Female painter, Codex Telleriano-Remensis, lower left corner of folio v (Biblioteca Medicea Laurenziana, Firenze, CC-BY-NC-SA 4.0).                                                   30 Albañil  El albañil tiene por oficio hacer mezcla mojándola bien, y echar tortas de cal, aplanarla y bruñirla bien. Él mal albañil por ser inhábil, lo que encala es atolondrado, ni es liso, sino hoyoso, áspero y tuerto. Translated by Rivera.  31 Pintor  El pintor es de su oficio saber usar de colores y dibujar, o señalar las imágenes con carbón, y hacer muy buena mezcla de colores, y saberlas moler muy bien y mezclar. El buen pintor tiene buena mano y gracia en el pintar, y considera muy bien lo que ha de pintar, y matiza muy bien la pintura, y sabe hacer las sombras, y los lejos, y follajes. El mal pintor es de malo, y bobo ingenio, y por esto es penoso, enojoso, y no corresponde á la esperanza del que da la obra, ni da lustre a lo que pinta, y matiza mal, todo va confuso, ni lleva compás, ó proporción lo que pinta, por pintarlo de prisa. Translated by Rivera.  184  It should be noted that after giving an account of these trades, he describes "wise men" as skilled and knowledgeable, like a "path and guide for others" (Sahagún), characteristics that ideally describe an architect:  Wise men [Architects and Engineers] 32 A wise man is like fire or a large ax, a gleaming mirror polished on both sides, a good example for others; skilled and knowledgeable, and is like a path and guide for others. The good wise man, as a good physician, remedies things well, and gives good advice and instruction, guides and enlightens others, because he is trustworthy and credible, and sensible and accurate in everything. So that things are done well, he gives order and coherence, which satisfies and pleases all; he responds to the desire of those who ask him; he encourages all and assists with his knowledge. The bad wise man is like bad doctor, foolish and lost, friend of the name "wise man" and vain glory; and, for being a fool, he is the cause of many evils and big mistakes, he is dangerous and shameless, deceiver or trickster.  These descriptions portray a complex building execution system that included talented craftsmen and "wise men" (Figure 5.40). Without these, it is difficult to imagine how they could have performed the many urban and architectural works that the Spanish found throughout the Aztec Empire. Moreover, without these indigenous hands, it would not have been possible to construct such a large number of buildings, churches and monasteries during the 16th century (Benítez 1992:20). The art and architecture performed with Indigenous hands and European ideas produced a style of art called tequitqui, which is the Indigenous redefinition and reinterpretation of European art and architecture (Aguilar 2007:389). This style found its greatest manifestations in façade reliefs, mural paintings, atrial crosses and sculptures.                                                   32 De los Sabios  El sabio es como lumbre o hacha grande, espejo luciente y pulido de ambas partes, buen dechado de los otros, entendido y leído; también es como camino y guía para los demás. El buen sabio, como buen médico, remedia bien las cosas, y da buenos consejos y doctrina, conque guía y alumbra a los demás, por ser él de confianza y de crédito, y por ser cabal y fiel en todo; y para que se hagan bien las cosas, da orden y concierto, con lo cual satisface y contenta á todos; respondiendo al deseo esperanza de los que se llegan a él, a todos favorece y ayuda con su saber. El mal sabio es como mal médico, tonto y perdido, amigo del nombre de sabio y de vana gloria, y por ser necio es causa de muchos males y de grandes errores, peligroso y despenador, engañador o embaucador. Translated by Rivera. 185    (a) (b)  (c) Figure 5.40. (a) Strategizing for a battle with a plan of the building they intend to attack, folio 33r (Biblioteca Medicea Laurenziana, Firenze, CC-BY-NC-SA 4.0); (b) Preparing colours for scribe seen writing on paper, (Biblioteca Medicea Laurenziana, Firenze, CC-BY-NC-SA 4.0);(c) The people of Xochimilco building a causeway, depicted by several tradesmen, tools (including a measuring cord) and a group of three men receiving instructions from the emperor, Durán, plate 13, chapter 8 (Biblioteca Nacional de España, CC-BY-NC-SA 4.0).   186  "There is no doubt that the astounding craftsmanship that the Spaniards encountered in New Spain was rooted in a very ancient and rich artistic tradition, and thereafter it could never be fully suppressed. The friars, who made themselves responsible for the reconstruction of sacred spaces, therefore used Indian labour to build and adorn the churches and convents of the new Spanish colony (Aguilar 2007:390).  This system was accompanied by materials, tools and construction techniques that are still used today. Materials such as soil, rocks and wood, are still commonly employed, as are tools such as the plumb, water level, ruler, compass, square, trowel, wedge and the lever.  5.5.2 Construction Materials  Construction materials uncovered during the five seasons of Temple Mayor excavations are consistent with the data obtained from 16th-century historical sources. The type of rocks found at the archaeological site include volcanic, basalt andesite and limestone. They are found in widely varying shapes and sizes, meeting a variety of architectural functions (López Luján, Torres and Montúfar 2003:140) (Figure 5.41).  Soil was used primarily as a base material for construction fill of the religious buildings of Tenochtitlan. Whenever the temples were expanded, they required huge volumes of soil mixed with stone just to bury the previous stage. Soil was also used, although to a much lesser extent, as plaster for walls with murals (López Luján, Torres and Montúfar 2003:148).  Lime from limestone and volcanic sand were also essential in the construction the buildings. They were used in the preparation of the plaster and stucco covering the floors, stairs, walls, internal walls, sidewalks and drainage pipes (López Luján, Torres and Montúfar 2003:150).  187   Figure 5.41. Enlargement of a temple in Tlatelolco utilizing several trades and construction materials, Codex Azcatitlan, folio 14 (Bibliothèque Nationale de France, CC-BY-NC-SA 4.0).  As for wood, archaeologists have unearthed numerous foundation pegs in Stage II of the Templo Mayor in the city of Tlatelolco. Other varied uses of wood in construction were recorded by Sahagún. He identifies, among other architectural elements, columns (cuauhtlayahuallo), lintels (calíxcuatl, ilhuicatl), stakes (tlaxichtli), jambs (tlaquetzalli, tlaquetzamimilli, tlaxílotl), the planks which are placed between the stone foundation and adobe wall (cuauhtepánitl), columns (cuauhtectli, cuauhmimilli), beams that rest on walls and support other beams (cuauhtentli), planks (huapalli), and boards (López Lujan , Torres y Montúfar 2003:152-154).  5.5.3 Construction Tools  Regarding construction tools, Guerra states:  The Aztec mason (tlahquilqui) seems to have used most of the building instruments of the "Old World:" the plumb (temetztepilolli), water level (aztecatl), ruler (tlahuahuanaloni), compasses (tlayolloanaloni), square (tlanacazanimi), trowel (tenexzasoloni), wedge (tlatilli), and the lever (quamniztli). The stonecutter (tetlapanqui) used special axes made of extremely hard stone (Guerra 1969:43) (Figure 5.42).  188    (a) (b) Figure 5.42. (a) Carpenter tools, folio 17r; (b)Stonemason tools, folio 20r33, (Biblioteca Medicea Laurenziana, Firenze, CC-BY-NC-SA 4.0).  These Nahuatl terms were also included in the Vocabulario en lengua castellana y mexicana y mexicana y castellana published by Alonso de Molina in 1571. For example, he defines:  "Quauhximaloyan" as a carpenter shop, or a neighborhood [calpulli] of carpenters (Molina f. 87v. col. 2)  "Quammimilli "as a round log or wooden column (f. 85r. col. 1.)  "Tenexzasoloni" as a mason's trowel or bricklaying tool (f. 99r. col. 2).                                                   33 Even though metal tools, such as saws, were introduced by the Spanish, similar tools made of obsidian (utilizing the same technique used for weapons) might have been used. 189   Figure 5.43. Arte de la lengua mexicana y castellana published by Alonso de Molina in 1571 (Newberry Library, CC-BY-NC-SA 4.0).  Finally, there is evidence of the use of a measuring cord before the Spanish arrival. Christopher Powell performed an analysis of the ethnohistoric and ethnographic descriptions of the uses of the measuring cord and interpreted their symbolic significance within architecture. He observed that first the measuring cord was repeatedly used to create sacred space in the ethnohistoric examples. For example, in Codex Vindobonensis Mexicanus 1,34 the measuring cord is used in the creation stage at least ten times. Second, four of the ceremonies from the ethnohistoric accounts and all of the examples from the Vindobonensis involving the measuring cord were also depicted within architecture. "In the ethnohistoric accounts, these associations include: performance in courts in front of temples (creating a quincunx or sacred space in front of or near the temple); purification of temples; or refurbishing of temples." Based on these observations, he proposed that the two figures are utilizing the measuring cord to actually lay out sacred architecture (Powell n.d.:14-15) (Figure 5.44).                                                  34 Probably the codex belonged originally to Lord 4 Deer (Iya Quicuaa), the last pre-Hispanic ruler of Tilantongo, and was presented to the Spaniard conquistadores shortly after their arrival (1519). In 1521, it was already in Europe (Maarten E. R. G. N. Jansen  2006). 190    (a) (c)   (b) (d) Figure 5.44. (a) Folio 10 displaying gods, mountains, buildings and figures with measuring cord on lower right; (b) detail of folio 10; (c) Folio 5 displaying gods, mountains, buildings and figures with measuring cord on middle right section; (d) detail of folio 5; all Facsimiles of the Codex Vindobonensis Mexicanus 1, Kingsborough Volume II (FAMSI CC-BY-NC-SA 4.0).  5.6 Chapter Summary  This chapter demonstrated how the Aztec knowledge of astronomy, mathematics and geometry was applied to create their horizon reference systems at calendrically significant intervals (Chapter 4) as well as to lay out their urban centres and architectural structures (Chapter 3), since a set of design principles had to be followed to achieve the relationship between the buildings and the landscape. These principles involved charting the movement of the Sun, calculating linear distances, measuring angles and utilizing geometric principles in their designs.  191  Even though this design knowledge was not specifically described in the ethno-historical sources that survived the Conquest, this information can be inferred from several sources including: pictorial administrative manuscripts (Chapter 2) that have been studied by mathematicians; measurements of the direction of the urban axes of a large number of churches —the colonial successors of temples— that have been surveyed by archaeoastronomers in Central Mexico; and underlying regulating lines in both monumental sculpture and architecture deduced by architects.  Furthermore, a sophisticated design and construction system can also be extracted from ethnohistorical and linguistic sources (Chapter 2). Similar to the contemporary architectural and building practice of contemporary Western civilizations, this building execution system required skilled tradesmen, "wise men" [architects and engineers], materials and tools that allowed them to construct buildings and cities throughout their empire.  Consequently, this chapter contributed essential information for the analysis of Aztec architecture and urban planning that was utilized for the archaeoastronomical analyses of the pre-Aztec and Aztec sites selected for this research (Chapter 6), as it established the role of astronomy, the symbolic importance of the Sun rising between the temples of the Huey Teocalli of Tenochtitlan, the role of precise measurements and the application of geometric design principles. 192  Chapter 6: Archaeoastronomical Analyses of Selected Pre-Aztec and Aztec Sites  6.1 Introduction  Research carried out in the previous chapters demonstrated that cultural aspects such as religion, geography, astronomy, mathematics and geometry were embedded in the design of their urban centres and architectural structures. Each of these chapters provided the cultural information that needed to be taken into account for the archaeoastronomical analyses. The ethnohistoric sources contributed the architectural and urban information contained in manuscripts, sculpture and oral history (Chapter 2); the typological analysis highlighted the main double temple teocalli as a distinct Aztec architectural type in Central Mexico (Chapter 3); the explanation of Aztec cosmovision provided an understanding of the significance of mountains, caves and bodies of water; the findings of high mountain archaeology demonstrated the relevance of certain topographic features within the sacred landscape and Cerro Tlaloc (Chapter 4); astronomy outlined the role of the heavenly bodies, including the cyclical movement of the Sun and Venus and their role in Aztec calendric systems; mathematics demonstrated the utilization of measurement units and angular systems; and geometry validated the use of axes and regulating lines (Chapter 5). Consequently, the aim of this chapter is to demonstrate how the cultural information extracted from traditional and non-traditional ethnohistoric sources converged and overlapped with the archaeoastronomical analyses—the core of the radial methodology — in order to understand the design principles of Aztec architecture and urban planning.  This chapter is divided in two main sections. The first section illustrates with a case study the methodology that was applied in the archaeoastronomical analyses through a series of images and detailed explanations. Since this methodology considered information ranging from religious, mathematic and geometric cultural knowledge to site-specific topographic and solar information, the analyses followed the same format even though the amount of cultural information varied from site to site. In spite of this unbalance, the topographic and solar information of each site always included: the seasonal-and-hourly positional changes of the Sun throughout the year; the rising and setting times of the Sun during the solstices, equinoxes and 193  alignment dates; the altitude and azimuth of the Sun on these dates; and, finally, the topographic features in the local horizon of each site such as mountains, caves and springs.  The second section is a summary of the archaeoastronomical-topographic analyses of two pre-Aztec sites, Teotihuacan and Tula, and five Aztec sites with surviving archaeological remains of a double temple teocalli: Tenochtitlan, Tlatelolco, Tenayuca, Santa Cecilia Acatitlan and Teopanzolco. The analyses of each of these sites includes four subsections: a historical background; a summary of previous archaeoastronomical research and theories that have been proposed to explain its orientation; a discussion of the digital archaeoastronomical analyses and research findings; and a selection of images to illustrate the analyses at the end of each section to allow a continuous reading flow.    The archaeoastronomical-topographic analyses of each site consisted of: identifying the site in the context of the Valley of Mexico, defining the major alignment of the site, calculating the visibility of major topographic features, exploring with precision each significant direction (site alignment, solstices and equinoxes), building an horizon calendar based on identified alignments and summarizing the findings of each site. These summaries contain the same type of information that allows the comparison among sites and the identification of their similarities and differences.   Chapter 6 concludes with a discussion of the main urban and architectural design principles deduced from the archaeoastronomical-topographic analyses and how they were applied in main Aztec cities and their respective Huey Teocallis.  6.2 Methodology  As a means to understand each archaeological site from an architectural and urban design point of view, a consistent methodological approach was developed that would allow a systematic, and importantly, a precise analysis of the astronomical and topographic aspects of each site. Archaeoastronomical research carried out in the last four decades had already revealed that Mesoamerican civil and ceremonial buildings were mostly oriented towards the position of the 194  rising or setting Sun on the local horizon on certain dates of the tropical year (Aveni and Hartung 1986, 2000; Aveni 2001, 2003; Tichy 1990; Galindo 1994; Šprajc 2001a, b, 2008) (Figure 4.7). These dates have been interpreted in relation to the cultivation cycle and the counting of the days in the calendrical system. There is historical and anthropological evidence that these dates marked four crucial moments in the cultivation cycle of maize corresponding to the preparation of farmland in February, the start of the rainy season and the time of planting at the beginning of May, ripening of the first ear August and the end of the rainy season and the beginning of the harvest at the beginning of November. One of the characteristics of these dates is that they are separated in intervals of 260 days (Chapter 4:132), the duration of the ritual cycle in the Tonalpohualli calendar (Šprajc 2008:237). Based on these significant dates, several archaeoastronomers have reconstructed possible horizon calendars utilizing prominent peaks on the horizon as natural markers of sunrises and sunsets in calendrical significant intervals of 13 or 20 days (Aveni and Hartung 1986; Tichy 1990; Aveni 2003; Šprajc 2001a, b, 2008) (Chapter 4:136). Since the average length of a year is 365.2422 days, these horizon calendars were necessary to adjust to the 20-day months (veintenas) of the cempoallapohualli (Johansson 2005:149).  The digital archaeoastronomical analyses for this research built upon the observational calendar concepts developed by these archaeoastronomers. However, it expanded these concepts by exploring the relationship between architecture and local topography in addition to the position of the Sun on certain dates within the local horizon (Chapter 4:136). Furthermore, it also considered a very dissimilar corpus for each site, from religious myths to site-specific astronomical information to topographic features.  Precise solar positions were also calculated, given that the Sun is not a point but a circular disk with an angular diameter of 32' of arc. The edge is called the limb; sunrise and sunset respectively occur with the first and last appearances of the upper limb of the solar disk (Kaler 2002:193). Hence, sunrise/sunset solar data —azimuth, altitude, date and time— can be calculated either for the astronomical horizon or for the local horizon where local topography must be taken into account (Kaler 2002:200). Consequently, this research had to calculate both sets of data due to the complexity of the topography in the Basin of Mexico (Chapter 4:139). 195    Figure 6.1. Sun path polar chart of Tenochtitlan, LAT 19.434921, LON -99.131362 on the astronomical horizon indicating the apparent seasonal-and-hourly positional changes of the Sun as the Earth rotates and orbits around the Sun. Azimuth angles run around the edge of the diagram; altitude angles are represented as concentric circular lines that run from the center of the diagram out; date lines start on the eastern side of the graph and run to the western side and represent the path of the Sun  on one particular day of the year; hour lines are shown as dotted blue lines that intersect the date lines and represent the position of the Sun at a specific hour of the day. The intersection points between date and hour lines give the position of the Sun (Polar chart by the University of Oregon, Solar Radiation Monitoring Laboratory).  196   Table 6.1. Rising and setting times for the Sun in Tenochtitlan, LAT 19.434921, LON -99.131362 on the astronomical horizon from January to June (2012). Cells in columns indicate the time when the first and last appearances of the upper limb of the solar disk occur during  sunrise and sunset respectively. (Table by the Astronomical Applications Department of the U.S. Naval Observatory Data Services).   Jan. Feb. Mar. Apr. May June Day Rise Set Rise Set Rise Set Rise Set Rise Set Rise Set h m h m h m h m h m h m h m h m h m h m h m h m 1 710 1810 711 1829 656 1842 630 1851 608 1900 558 1911 2 711 1810 711 1830 655 1842 629 1851 607 1900 558 1912 3 711 1811 711 1830 654 1843 628 1851 607 1900 557 1912 4 711 1811 710 1831 653 1843 627 1852 606 1901 557 1913 5 712 1812 710 1831 653 1843 627 1852 606 1901 557 1913 6 712 1813 710 1832 652 1844 626 1852 605 1901 557 1913 7 712 1813 709 1832 651 1844 625 1852 605 1902 557 1914 8 712 1814 709 1833 650 1844 624 1853 604 1902 558 1914 9 713 1815 708 1833 649 1845 623 1853 604 1902 558 1914 10 713 1815 708 1834 649 1845 622 1853 603 1903 558 1915 11 713 1816 707 1834 648 1845 622 1853 603 1903 558 1915 12 713 1817 707 1835 647 1846 621 1854 602 1904 558 1915 13 713 1817 706 1835 646 1846 620 1854 602 1904 558 1916 14 713 1818 706 1836 645 1846 619 1854 602 1904 558 1916 15 713 1818 705 1836 644 1846 619 1854 601 1905 558 1916 16 713 1819 705 1837 644 1847 618 1855 601 1905 558 1916 17 713 1820 704 1837 643 1847 617 1855 600 1906 559 1917 18 713 1820 704 1838 642 1847 616 1855 600 1906 559 1917 19 713 1821 703 1838 641 1847 616 1856 600 1906 559 1917 20 713 1822 702 1838 640 1848 615 1856 600 1907 559 1917 21 713 1822 702 1839 639 1848 614 1856 559 1907 559 1918 22 713 1823 701 1839 638 1848 613 1857 559 1908 600 1918 23 713 1824 700 1840 638 1848 613 1857 559 1908 600 1918 24 713 1824 700 1840 637 1849 612 1857 559 1908 600 1918 25 713 1825 659 1840 636 1849 611 1858 558 1909 600 1918 26 713 1825 658 1841 635 1849 611 1858 558 1909 601 1918 27 713 1826 658 1841 634 1849 610 1858 558 1910 601 1919 28 712 1827 657 1841 633 1850 610 1859 558 1910 601 1919 29 712 1827 656 1842 632 1850 609 1859 558 1910 601 1919 30 712 1828   632 1850 608 1859 558 1911 602 1919 31 712 1828   631 1850   558 1911   Note: Hours in bold indicate rising (559) and setting (1918) times on June 21, 2012.  197  Table 6.2. Altitude and azimuth for the Sun in Tenochtitlan, LAT 19.434921, LON -99.131362 on the astronomical horizon on June 21st, 2012. Sunrise occurs between 6:00 and 6:10 when the Sun rises from the horizon at an azimuth between 64.8 and 65.6. (Table by the Astronomical Applications Department of the U.S. Naval Observatory Data Services).  h  m Altitude Azimuth  h  m Altitude Azimuth  h  m Altitude Azimuth 5:10 -11.1 60  10:10 55.3 76.6  15:10 54.6 283.4 5:20 -9.1 61.1  10:20 57.6 76.6  15:20 52.3 283.5 5:30 -7 62.1  10:30 59.9 76.6  15:30 50 283.6 5:40 -4.9 63  10:40 62.2 76.4  15:40 47.8 283.8 5:50 -2.8 63.9  10:50 64.5 76.1  15:50 45.5 284.1 6:00 -0.1 64.8  11:00 66.8 75.7  16:00 43.2 284.3 6:10 1.8 65.6  11:10 69.1 75  16:10 40.9 284.6 6:20 3.8 66.4  11:20 71.3 74.1  16:20 38.6 285 6:30 5.9 67.2  11:30 73.6 72.8  16:30 36.3 285.3 6:40 8.1 67.9  11:40 75.8 71  16:40 34.1 285.7 6:50 10.2 68.6  11:50 78 68.3  16:50 31.8 286.1 7:00 12.4 69.2  12:00 80.2 64.2  17:00 29.6 286.5 7:10 14.6 69.9  12:10 82.3 57.6  17:10 27.3 287 7:20 16.8 70.5  12:20 84.1 46.2  17:20 25.1 287.5 7:30 19 71.1  12:30 85.5 25.8  17:30 22.8 288 7:40 21.3 71.6  12:40 86 354.9  17:40 20.6 288.6 7:50 23.5 72.1  12:50 85.2 326.7  17:50 18.4 289.1 8:00 25.7 72.6  13:00 83.6 309.6  18:00 16.1 289.7 8:10 28 73.1  13:10 81.6 300  18:10 13.9 290.3 8:20 30.3 73.6  13:20 79.5 294.3  18:20 11.7 291 8:30 32.5 74  13:30 77.4 290.7  18:30 9.6 291.6 8:40 34.8 74.4  13:40 75.1 288.4  18:40 7.4 292.3 8:50 37 74.8  13:50 72.9 286.7  18:50 5.3 293.1 9:00 39.3 75.2  14:00 70.6 285.6  19:00 3.2 293.8 9:10 41.6 75.5  14:10 68.4 284.7  19:10 1.2 294.6 9:20 43.9 75.8  14:20 66.1 284.2  19:20 -1.3 295.5 9:30 46.2 76  14:30 63.8 283.8  19:30 -3.5 296.3 9:40 48.5 76.2  14:40 61.5 283.5  19:40 -5.6 297.3 9:50 50.7 76.4  14:50 59.2 283.4  19:50 -7.7 298.2 10:00 53 76.5  15:00 56.9 283.4  20:00 -9.7 299.2 Note: Altitude is the angle up from the horizon. Azimuth is the angle along the horizon with respect to true north, with zero degrees corresponding to north, and increasing in a clockwise fashion. The apparent position of the Sun at a given time is defined by these two angles.  198  If sites were in a flat location, this information could have been enough for the analyses, but they were situated within geographic areas filled with very distinct topographic features specific to the Trans-Mexican Volcanic Belt (TMVB). Few regions in the world exhibit such a variety of volcanic landforms as the TMVB, which include binary volcanic systems, volcanic fields and lava caves. An example of these landforms are the Popocatepetl-Iztaccihuatl, the Ajusco–Xitle and the Sierra Negra–Pico de Orizaba binary systems in which one volcano is active and the other is inactive (Figure 6.2). Despite their proximity, these binary volcanoes are in different states of preservation because they were formed during different geological periods; some are small and perfect as the young cone Xitle (2400 years old), while others are eroded by the impact of several glaciations such as the Iztaccihuatl (30 million years old). The mountains that delimit the Basin of Mexico to the west and the mountain ranges of Las Cruces and Río Frío (Cerro Tlaloc (also known as Mount Tlaloc, Figure 4.15), Cerro Telapon and Cerro Papayo) to the east, are also volcanoes that lost their craters, original conical shapes and all eruptive systems through time (Chapter 4:139) (Montero 2004:2-4).   Figure 6.2. View of the binary volcanic system composed by the Volcán Iztaccihuatl and the Volcán Popocatepetl—with a fumarole coming out from its cone—seen from the tetzacualco located on the summit of Cerro Tlaloc. The closer mountain to the right is Cerro Telapon (Photograph by José Luis – CC:BY).  This complex landscape has been a challenge to archaeoastronomers as there is an abundance of topographic features that are not easy to identify due to the thick layer of smog that frequently covers the basin of Mexico or due to their underground location, for example caves or water springs. Furthermore, most sites are situated in areas that have been engulfed by the exorbitant 199  growth of Mexico City in the 20th century and are often in "peripheral" hard-to-reach places, dangerous due to their economically and socially marginalized population. Fieldwork is therefore extremely difficult (Broda 1991b:81). Archaeoastronomers have also been limited by the inherent constraints of printed topographic maps which might have covered some areas and not others, might have been in a smaller scale, or might not have contained the required information relevant to their analyses. In addition to these challenges, some buildings, such as the double teocallis, were built in several construction stages (Chapter 3:87). For example, in the Great Teocalli of Tenochtitlan, the remains of these stages have also subsided unevenly because of the difference in the solidifying of the subsoil clays, which have lead to different azimuth measurements. These slight variations (±1° from average azimuth) have resulted in diverse interpretations of the orientation of the Great Teocalli (Šprajc 2001: 384-390). Despite these variations, there is a widespread agreement that the location and orientation of the Great Teocalli was determined by astronomical and topographic considerations. However scholars differ in the interpretation of these variations, as they disagree on the observational techniques the Aztecs utilized to observe the Sun rise between the double teocallis described by Motolinía, but because we do not know from which location they were observed, or the exact height of these buildings, some archaeoastronomers had to make estimates (Figure 6.3 and Figure 5.8).   Figure 6.3. Interpretation of the Sun rising in the notch of the Great Temple on March 21st by Aveni which presupposes the height of the Templo Mayor and the existence — at a certain distance and height — of a circular temple where this event was viewed (Aveni and Gibbs 1978: Figure 4).  200  In order to overcome most of these challenges —and utilize as a basis for further exploration the archaeoastronomical studies carried out by scholars such as Aveni (1975, 2001), Aveni and Hartung (1986), Broda (1993), Galindo (1994), Šprajc (2001a, b, 2008), Tichy (1990) and Montero (2004), among others— an interdisciplinary methodology was developed for this digitally-based research that combined the vast corpus of research on Aztec culture with digital mapping, solar charting, viewshed calculating, geo-tagging and collaborative mapping applications. These applications provided the accuracy this research required, for they are based on high-resolution superimposed images of Earth obtained from satellite imagery, aerial photography and the GIS 3D globe. Google Earth, the virtual globe, and the map and geographical information applications use the digital elevation model (DEM) data collected by NASA's Shuttle Radar Topography Mission (SRTM); its internal coordinate system employs the geographic coordinates (latitude/longitude) on the World Geodetic System of 1984 (WGS84) datum, the same datum used by GPS (Zomrawi et al. 2013:7). Besides utilizing the information supplied by Google Earth, the solar charting and viewshed calculating applications also take into consideration the curvature of the Earth and the average refraction of a certain area so as to obtain results closer to reality. The obliquity (angle between the ecliptic and the equator that has been steadily decreasing by approximately 40 seconds of arc per century) was disregarded as it has barely shifted since A.D. 1500 (Aveni 2001:103). In addition, the dates utilized in the solar charting applications for this research correspond to the year 2014, so ±1 day variations can be expected in the calculations of dates. In conjunction, these applications offer unparalleled precision and information compared to printed maps, as sites can be analyzed at different scales; relationships between sites, other sites and nearby or distant topographical features can be explored; and a variety of locally relevant information can be accessed for any given site.   Although there is a wide diversity of research performed by archaeoastronomers on several sites —particularly in Teotihuacan and Tenochtitlan— this digitally-based independent exploration did not reference horizon calendars published by archaeoastronomers to prevent inadvertently influencing findings of this research (Tichy 1990, Šprajc 2001a). It also did not utilize any of the publicly available plans of the archaeological sites, since they are frequently inaccurate, confuse true magnetic north with true north or vice versa, and sometimes draw structures as if they had 201  already been excavated; hence, they are not accurate enough for digital astronomical and topographic analyses.  The digital archaeoastronomical analyses of this research only focused on the orientation of the main structure of the site, as ethno-historical sources indicate that the foundation of a city was followed by the construction of the temple to the patron deity(s) of the ethnic group, as well as by the respective consecration ceremonies (Florescano 2006). This temple served as central point of the axis mundi (Chapter 4:Figure 4.5) that divided the physical space in quadrants bounded by the solstice points of the rising and setting Sun (Chapter 4:Figure 4.6).  In Aztec sites, this temple is the double teocalli, but in Pre-Aztec sites, this temple corresponds to the main teocalli on the urban east-south axis of the site. Since the main axes of sites in Central Mexico exhibit an easterly deviation from the true north (Aveni 2001:233) (Chapter 4:Figure 4.7), this research introduced the utilization of the concept of "urban axes" to refer to this azimuthal deviation and clearly distinguish it from true, magnetic or grid directions. Furthermore, since the same structure can exhibit slight variations on each of its sides —either due to pre-Hispanic construction methods (Chapter 5:178) or due to restoration or reconstruction work—the mean alignment present on both the main structure and the site was selected for the analyses.  Regarding the digital topographic analyses, this research considered not only the visible prominent peaks on the horizon as calculated by the viewshed applications, but also other topographic features such as mountains, valleys, caves, lakes, rivers and springs (Chapter 4:Figure 4.13 and Figure 4.14). It also kept the names of volcanoes, mountains and caves in Nahuatl or Spanish to facilitate their identification.  Since the objective of this research was to gain an understanding of Aztec architecture and urban planning, both Pre-Aztec and Aztec sites were analyzed. The pre-Aztec sites of Teotihuacan and Tula were chosen due to their historical and symbolic relation to the cultures in Central Mexico as archaeologists, archaeoastronomers, ethnographers, and historians have demonstrated (Carrasco et al. 2000:12) (Chapter 3:121) The Aztec archaeological sites of Tenochtitlan, 202  Tlatelolco, Tenayuca, Santa Cecilia Acatitlan, and Teopanzolco (Chapter 2:68) were selected based on the following criteria:  1. They must have some uncovered archaeological remains. 2. They should lie within an archaeological zone  of the Instituto Nacional de Antropología e Historia (INAH). 3. They should be identified by scholars as Aztec sites. 4. They should have a teocalli, since it is a unique Aztec building type (Chapter 3:87).   In order to perform the complex analyses that each site required, an application capable of performing geometric, solar and topographic analyses at the same time was developed for this dissertation. Even though Google Earth had the capability of making some of these analyses, it lacked the precision and interactivity required for this purpose.  Eventually, the analyses required the utilization of several applications: Google Earth, a solar charting application (SCA), a topographic application (TA), an open-content collaborative application (Wikimapia), a geo-location-oriented photo sharing site (Panoramio) and a custom geometric application (CGA) that could run over all of them. Google Earth located with precision sites and topographic features. The solar application provided solar information that could be controlled with exactitude by the minute. The topographic application gave altitude, distance and visibility of topographic features from a certain location. The custom geometric application (CGA) allowed to view the relationships between the site, its topography and the movement of the Sun as it could zoom in and out, draw reference lines, measure and graphically annotate the site being analyzed at a given moment without affecting the underlying application. This custom application also provided the capability to work in the same scale between digital maps and applications which was critical for obtaining the most precise information. Wikimapia, Panoramio and Google aided with the identification of sites and provided contextual information of topographic features, as many of these applications rely on databases which might not have complete —or culturally relevant— data.   203  Since the aim of the analyses was to acquire consistent data that could be utilized for comparison among sites, a detailed step-by-step systematic and replicable methodology was developed. Consequently, each site was taken through a series of steps, data was recorded and findings were documented for each site.  6.3 Methodological Steps for the Digital Topographic and Archaeoastronomical Analyses  In order to demonstrate this methodology, a summary of the steps that correspond to the analysis of Tenochtitlan are further described in the next section. For the purpose of clarity, they are presented in a linear form, even though the inherent process of the radial methodology involved continuous cross-referencing solar, topographic, cultural and ethnohistorical information. Since these steps focus on the explanation of the methodology, a further discussion about the site of Tenochtitlan was included in its corresponding section later in this chapter.  1. Define precise latitude, longitude and azimuth of the major east-west axis of the main teocalli of site ± 0.5° (Figure 6.4).  This step involved drawing reference lines with the custom geometric application (CGA) on identifiable walls or platforms of the archaeological remains of the Great Teocalli displayed on Google Maps. This resulted in the values of 19.434921° latitude (LAT) and -99.131362° longitude (LON).  The process for determining the major east-west axis alignment of the Great Teocalli was more complex since its azimuths varied from 95.71° to 97.38° among its different construction stages, resulting in a mean value of 96.54°. These calculations were consistent with the measurements taken by Šprajc, who calculated a mean of 96.5° ± 0.5° on Stage II and 96.67° ± 0.5° on subsequent stages (2001a:388). It was also similar to the 96.7° mean calculated by Aveni, Calnek and Hartung in 1988 (294). Therefore, the azimuth of the major east-west of the Great Teocalli was rounded to 96.5° ± 0.5°, thus defining the urban east west axis for the digital analyses.   204   Figure 6.4. Archaeological remains of the Great Teocalli of Tenochtitlan, scale 1:200. The streets of present day Mexico City follow the same azimuthal direction of 96.5° ± 0.5° of the Great Teocalli (Map data: Google Earth).205  2. Identify prominent peaks around site, (Figure 6.5), and calculate azimuth, apparent altitude and distance of the prominent peaks on the horizon viewed from site (Table 6.3).  Table 6.3. Prominent peaks on the horizon viewed from Tenochtitlan Azimuth/Apparent Altitude Topography Distance 5°/2.37° Pico Tres Padres 17 km 131°/2.3° Volcán Popocatepetl 70 km 140°/0.74° Sierra de Santa Catarina 17 km 141°/0.6° Cerro Xaltepetl 17 km 164°/2.03° Volcán Tlaloc 38 km 186°/1.6° Cerro Acopiaxco 35 km 196°/2.27° Volcán Pelado 33 km 208°/3.24° Volcán Ajusco 29 km 252°/2.1° Cerro La Campana  30 km 319°/0.46° Cerros Los Baños 59 km 206   Figure 6.5. Prominent peaks around Tenochtitlan, scale 1:10,000 Yellow triangles, which indicate larger peaks, are identified as "volcán" (volcano), while green triangles, which indicate smaller peaks, are identified as "cerro" (mountain), regardless of their geological origins (Map data: Google Earth). 207  3. Calculate viewshed of site (Figure 6.6).  This viewshed calculation was necessary because not all prominent peaks might be visible from the site (Tenochtitlan) due to the presence of local topographic features that might obstruct the view to a prominent peak or due to the curvature of the Earth. Likewise, prominent peaks located farther from local viewshed might be visible in clear atmospheric conditions. 208   Figure 6.6. Viewshed of Tenochtitlan shown as red shaded areas and prominent peaks on the horizon, scale 1:10,000 (Map data: Google Earth and TA). 209  4. Create a 6.5° alignment reference diagram of the site (indicating true north-south-east-west axes, solstitial/equinoctial axes and urban north-south-east-west axes) and superimpose it on topographic landscape around site (Figure 6.7). Repeat the same steps for a 7.0° alignment reference diagram.  This step involved creating an alignment reference diagram of the site (Tenochtitlan) in AutoCAD that was later utilized in the custom geometric application (CGA) so it could be superimposed on Google Earth (with the viewshed data imported from the TA) concurrently on the same screen. While CGA kept the size and resolution of the diagram, Google Earth was able to increase or decrease its scale as a result of zooming in or out. The results of these analyses only served as a guideline for further exploration as this reference diagram is only a geometric reference that did not consider the topographic altitude and the curvature of the Earth. 210   Figure 6.7 Alignment reference diagram superimposed on topographic landscape of Tenochtitlan. Tentative alignments to prominent peaks on the horizon can be observed on solstitial/equinoctial and urban axes, scale 1:10,000. (Map data: Google Earth, AutoCAD, TA and CGA).  211  5. Calculate solar elevation and azimuth angles for the dates when the 96.5° urban east-west axis aligns to the position of the rising Sun (instant when the upper limb of the solar disk touches the horizon) on the eastern horizon taking into consideration astronomical and local horizons (Figure 6.8). Repeat the same steps for a 97.0° urban east-west axis.  Considering that the astronomical horizon is the imaginary horizontal plane at a 90° angle from the observer's zenith (the point directly above the observer) and that the local horizon is the visible boundary between the Earth and sky, both sets of solar data needed to be calculated for the site (Tenochtitlan) with the SCA since they are different due to the topography of the Valley of Mexico (Figure 2.29). These calculations revealed that the Sun appeared in the intermediate point (19.391519°, -98.716064°) between the binary volcanic system of Cerro Tlaloc (also known as Mount Tlaloc) and Cerro Telapon on March 6 and October 7 utilizing the mean value of 96.5° and on March 4 and October 9 utilizing the value of 97° (calculations based on the year 2014). 212   Figure 6.8. Position of the rising Sun between Cerro Tlaloc (also known as Mount Tlaloc) and Cerro Telapon along the 96.5° urban east-west axis of Tenochtitlan considering topographic altitude and the curvature of the Earth. The thick yellow line indicates the sunrise azimuth in the astronomical horizon. The fine yellow line indicates the sunrise azimuth in the local horizon, which corresponds to the real position of the Sun viewed from the site (Map data: Google Maps, INEGI and SCA). 213  6. Calculate solar elevation and azimuth angles for the dates when the 96.5° urban east-west axis aligns to the position of the setting Sun (instant when the upper limb of the solar disk touches the horizon) on the western horizon taking into consideration astronomical and local horizons (Figure 6.9). Repeat the same steps for a 97.0° urban east-west axis. 214   Figure 6.9. Position of the setting Sun on nondescript topographic feature along the 96.5° urban east-west axis of Tenochtitlan considering topographic altitude and the curvature of the Earth. The thick red line indicates the sunset azimuth in the astronomical horizon. The fine red line indicates the sunset azimuth in the local horizon, which corresponds to the real position of the Sun viewed from the site (Map data: Google Maps, INEGI and SCA). 215  7. Locate the topographic feature where the 6.5° urban north axis of the site intersects with the northern local horizon by calculating its altitude and distance (Figure 6.10). Repeat the same steps for a 7.0° urban north axis.  This step involved calculating the distance and altitude of the topographic feature along the urban north axis of Tenochtitlan, taking into account the local viewshed, curvature of the Earth and refraction. This analysis revealed that the urban north axis of Tenochtitlan was the most prominent peak on the local horizon to the north, the highest peak of Pico Tres Padres, the same topographic-urban relationship that Teotihuacan has along its urban north axis with Cerro Gordo. 216   Figure 6.10. Alignment of Tenochtitlan to the highest peak of Pico Tres Padres (within the Sierra of Guadalupe) along its the urban north axis (marked on diagram as NE axis). This diagram contains three views from Tenochtitlan to the highest point of Pico Tres Padres: a 360° topographic panorama showing the alignment, a topographic profile section and an aerial view (Map data: Google Maps and TA). 217  8. Locate the topographic feature where the 96.5° urban east-west axis of the site intersects with the local eastern horizon by calculating its altitude and distance (Figure 6.11). Repeat the same steps for a 97.0° urban east-west axis.  This step involved calculating the distance and altitude of the topographic feature along the urban east of Tenochtitlan taking into account the local viewshed, curvature of the Earth and refraction. This analysis confirmed that the urban east axis of Tenochtitlan was to the intermediate point (19.391519°, -98.716064°) that marked the concave space between the binary volcanic system of Cerro Tlaloc and Cerro Telapon, thus framing the rising of the Sun on March 6 and October 7 (96.5°) or on March 4 and October 9 (97°). There is ethnohistorical and archaeological evidence that these two prominent peaks were an integral part of Aztec religion, as Cerro Tlaloc was called "Tlalocan" —house of the rain god— which was believed to be the origin of rain, mist, clouds and snow (Aveni, Calnek and Hartung 1988:298) (Chapter 4 Figure 4.14 and Figure 4.15).  218   Figure 6.11. Alignment of Tenochtitlan to the intermediate point (19.391519°, -98.716064°) between the binary volcanic system of Cerro Tlaloc and Cerro Telapon along its the urban east axis (marked on diagram as SE axis). This diagram contains three views from Tenochtitlan to Cerro Tlaloc and Cerro Telapon: a 360° topographic panorama showing the alignment, a topographic profile section and an aerial view (Map data: Google Maps and TA). 219  9. Locate the topographic feature where the 186.5° urban south axis of the site intersects with the southern local horizon by calculating its altitude and distance (Figure 6.12). Repeat the same steps for a 187.0° urban south axis.  This step involved calculating the distance and altitude of the topographic feature towards the urban south of Tenochtitlan taking into account the local viewshed, curvature of the Earth and refraction. This analysis revealed that the urban south axis of Tenochtitlan was to Cerro Acopiaxco, an inconspicuous cinder cone located on the massive Chichinautzin volcanic field, specifically on an area characterized by multiple caves of great extension, the same topographic-urban relationship that Teotihuacan has along its urban south axis to the Xometla caves. 220   Figure 6.12. Alignment of Tenochtitlan to Cerro Acopiaxco (within the Chichinautzin volcanic field and lava caves) along its the urban south axis (marked on diagram as SW axis). This diagram contains three views from Tenochtitlan to Cerro Acopiaxco: a 360° topographic panorama showing the alignment, a topographic profile section and an aerial view (Map data: Google Maps and TA). 221  10. Locate the topographic feature where the 276.5° urban west axis of the site intersects with the local western horizon by calculating its altitude and distance (Figure 6.13). Repeat the same steps for the 7.0° urban west axis.  This step involved calculating the distance and altitude of the topographic feature towards the urban west of Tenochtitlan taking into account the local viewshed, curvature of the Earth and refraction. This analysis confirmed that the urban west axis of Tenochtitlan was to a nondescript topographic feature between Cerro La Malinche and Cerro Geishto, thus making this location a difficult reference point for a horizon calendar. Even though this area has been inhabited by an otomí population since pre-Aztec times, it is neither mentioned in ethnohistoric sources nor has it any reported archaeological remains (Galindo 166). Even supposing a horizon calendar could have been built towards this direction, it is unlikely that this location served as a reference point because it is hard to distinguish it from other peaks within the mountain range. However, a Google Earth exploration with a three-dimensional model of the Great Teocalli by Blake and Rivera revealed that during sunset, the Sun illuminates with a spotlight effect the Great Teocalli, thus making it standout as in a theatrical stage with the Valley of Mexico as a background on April 6 and September 5 (96.5°) or on April 9 and September 3 (97°), an imposing view that Bernal Diaz del Castillo described when they entered Tenochtitlan (Chapter 2:61). 222   Figure 6.13. Alignment of Tenochtitlan to a nondescript topographic feature along its the urban west axis (marked on diagram as NW axis). This diagram contains three views from Tenochtitlan to Cerro Tlaloc and Cerro Telapon: a 360° topographic panorama showing the alignment, a topographic profile section and an aerial view (Map data: Google Maps and TA). 223  11. Locate the topographic features where the Sun rises during the solstices and equinoxes on the true eastern horizon from site, and plot these reference points along with main site alignment point in a 360° topographic panorama (Figure 6.14). Perform the corresponding calculations for the true western horizon.  This step involved calculating the distance and altitude of the topographic feature towards