1 Preface 2 Polyhedra, from Pythagoras to Alexander Graham
Bell 2.1 INTRODUCTION 2.2 NATURAL CRYSTALS 2.3 THE EARLIEST
POLYHEDRAL OBJECTS 2.4 THE ANCIENT GREEKS ON POLYGONS 2.5 THE ANCIENT GREEKS ON POLYHEDRA 2.6 ANCIENT POLYHEDRAL
MODELS 2.7 MEDIEVAL APPROACH 3 CONTRIBUTIONS FROM
THE ARABIC WORLD 3.1 PAOLO UCCELLO (ca. 1397–1475) AND THE
‘‘MAZZOCCHIO’’ 3.2 PDERO DELLA FRANCESCA (ca. 1420–1492)
AND HIS PERSPECTIVE LESSONS 3.3 LUCA PACIOLI (ca. 1445–1517)
AND THE MODEL APPROACH 3.4 LEONARDO DAVINCI (1452–1519) AND
THE LATTICE STRUCTURE 3.5 ALBRECHT DURER (1471–1528) AND
THE CLEARING OF POLYHEDRAL IMAGES 3.6 JOHANN NEUDORFER
(1497–1563) AND THE DDDACTBC MODEL 3.7 WENZEL JAMNITZER
(ca. 1508–1585) AND RENAISSANCE AESTHETICS 3.8 JOHANNES
KEPLER (1571–1630) AND POLYHEDRAL NOMENCLATURE VERSUS
COSMOLOGY 3.9 THE CHINESE ‘‘DEVIL’S WORK BALLS’’ 3.10 BROOK
TAYLOR (1685–1731) ON PERSPECTIVE PROJECTION OF POLYHEDRA 3.11 MAX BRUCKNER (1860–1934) AND HIS PAPER MODEL COLLECTION 3.12 ALEXANDER GRAHAM BELL (1847–1922) AND INVENTIVE
USE OF TETRAHEDRA 3.13 CONCLUSIONS 3.14 METHODOLOGY 3.15 ACKNOWLEDGMENTS 3.16 NOTES 3.17 INTRODUCTION 4 GOFF’S
LEGACY 5 ACKNOWLEDGMENTS 6 NOTES 6.1 BIBLIOGRAPHY 7 Louis Kahn and Space Frames 7.1 INTRODUCTION 7.2 CONCLUSION 7.3 ACKNOWLEDGMENTS 7.4 NOTES 8 Buckminster Fuller and the Relevant
Pattern 8.1 INTRODUCTION 8.2 THE RELEVANT PATTERN 8.3 NOTES 9 Polyhedral Structure 9.1 INTRODUCTION 9.2 AMERICAN EVANGELISM:
IMPROVISED RITUAL AND SPACE 9.3 THE REPRESENTAT8ON OF
MORALITY: THE CATHEDRAL AND THE HISTORICAL AVANT-GARDE 9.4 THE GLASS CHAIN BORN AGAIN 9.5 FROM BOULLEE TO
OLDENBURG: THE STRUCTURE IN A POSTMODERN CONTEXT 9.6 THE STRUCTURE AND AMERICAN MYTHOLOGIES OF NATURE 9.7 THE CONTEMPORARY PASTURE: A CATHEDRAL IN A PARK 9.8 CONCLUSION 9.9 NOTES 9.10 BIBLIOGRAPHY 10 Tetrahedral
Purity: The Javits Center 10.1 INTRODUCTION 10.2 ARCHITECTURE
AND POLITICS 10.3 10.4 CONCLUSION 10.5 BIBLIOGRAPHY 11 Double Curvature Space Frames Supported on Four Points: Design and
Construction of the International Plaza of Portopia ‘81 11.1 INTRODUCTION 11.2 CONCLUSION 11.3 CONCLUSION 12 Deconstruction of the Cube 12.1 INTRODUCTION 12.2 CONCLUSION 12.3 NOTES 13 The Polyhedral
World 13.1 INTRODUCTION 13.2 NOTES 14 Proportion and Symbolism in
Polyhedra 14.1 INTRODUCTION 14.2 CONCLUSION 14.3 SYMBOLISM
AND POLYHEDRA 14.4 The Constitution of Polyhedra and Their Interrelations 14.5 CONCLUSION 14.6 NOTES 15 The Structural Morphology of Basic
Polyhedra 15.1 INTRODUCTION 15.2 CONCLUSION 15.3 CONCLUSION 15.4 NOTES 16 Computer-Aided Processing of Polyhedric Configurations 16.1 INTRODUCTION 16.2 NOTES 17 Tensegrity: Theory and Application 17.1 INTRODUCTION 17.2 NOTES 18 Visual Morphology of Space Labyrinths:
A Source for Architecture and Design 18.1 INTRODUCTION 18.2 NOTES 19 Quasicrystal Architecture: The Space of Experience 19.1 INTRODUCTION 19.2 NOTES 20 Are Space Frames Habitablehabitable? 20.1 INTRODUCTION 20.2 INSIDE POLYHEDRA 20.3 20.4 THE HEXMOD: ITS MORPHOLOGY 20.5 CONCLUSION 20.6 NOTES 20.7 BIBLIOGRAPHY Index
1 2 Beyond the Cube
3
4 Beyond the Cube
5 The Architecture of
6 Space Frames and Polyhedra
7 J. Francois Gabriel
8 Editor
9
10 John Wiley & Sons, Inc.
11 NEW YORK / CHICHESTER / WEINHEIM / BRISBANE / SINGAPORE /
TORONTO
12 This text is printed on acid-free paper.
13 Copyright© 1997 by John Wiley & Sons, Inc.
14 All rights reserved. Published simultaneously in Canada.
15 Reproduction or translation of any part of this work beyond that permitted by Section 107 or
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unlawful. Requests for permission or further information should be addressed to the
Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY
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16 This publication is designed to provide accurate and authoritative information in regard to the
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17 Library of Congress Cataloging-in-Publication Data
18 Beyond the cube : the architecture of space frames and polyhedra / J. Francois Gabriel,
editor.
19 p. cm.
20 Includes index.
21 ISBN 0–471–12261–0 (cloth : acid-free paper)
22 23 1. Space (Architecture) 2. Space frame structures. I. Gabriel, J. Francois, 1930-.
24 NA2765.B45 1997 97–3547
25 721’ .042—dc21
26 Printed in the United States of America
27 Contents
28 Preface vii
29 J. Francois Gabriel, Syracuse University
30 Acknowledgments xiii
1.
Polyhedra, from Pythagoras to 31 Alexander Graham Bell 1
32 Jos Tomlow, Hochschule Zittau/Gorlitz, Germany
2.
Polyhedrality in the Architecture 33 of Bruce Goff. 35
34 Rollie Ristine
3.
Louis Kahn and Space Frames 127 35 Irene E. Ayad
4.
Buckminster Fuller and the Relevant Pattern 147 36 Arthur L. Loeb, Harvard University
5.
Philip Johnson’s Crystal Cathedral and the 37 Rhetoric of Its Free-Form Polyhedral Structure 161
38 Lawrence Davis, Syracuse University
6.
Tetrahedral Purity: The Javits Center 189 39 Matthys Levy
7.
Double Curvature Space Frames Supported 40 on Four Points: Design and Construction of the International Plaza of Portopia’81
211
41 Masao Saitoh, Nihon University
8.
Deconstruction of the Cube 229 42 Arthur L. Loeb, Harvard University
9.
The Polyhedral World 243 43 Pieter Huybers, Delft University of Technology
10.
Proportion and Symbolism in Polyhedra 281 44 Rene Motro, Universite de Montpellier
11.
The Structural Morphology of 45 Basic Polyhedra 301
46 Ture Wester, Royal Danish Academy of Fine Arts
12.
Computer-Aided Processing of 47 Polyhedric Configurations 343
48 49 Hoshyar Nooshin, with P. L. Disney and O. C. Champion, University of Surrey
13.
Tensegrity: Theory and Application 385 50 Ariel Hanaor, National Building Research Institute, Israel
14.
Visual Morphology of Space Labyrinths: 51 A Source for Architecture and Design 409
52 Haresh Lalvani, Pratt Institute
15.
Quasicrystal Architecture: 53 The Space of Experience 427
54 Tony Robbin
16.
Are Space Frames Habitable? 439 55 J. Francois Gabriel, Syracuse University
56 Contributors 495
57 Index 499
