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 2.8 CONTRIBUTIONS
FROM THE ARABIC WORLD 2.9 PAOLO UCCELLO (ca. 1397–1475)
AND THE ‘‘MAZZOCCHIO’’ 2.10 PDERO DELLA FRANCESCA (ca.
1420–1492) AND HIS PERSPECTIVE LESSONS 2.11 LUCA PACIOLI (ca.
1445–1517) AND THE MODEL APPROACH 2.12 LEONARDO DAVINCI
(1452–1519) AND THE LATTICE STRUCTURE 2.13 ALBRECHT
DURER (1471–1528) AND THE CLEARING OF POLYHEDRAL IMAGES 2.14 JOHANN NEUDORFER (1497–1563) AND THE DDDACTBC MODEL 2.15 WENZEL JAMNITZER (ca. 1508–1585) AND RENAISSANCE
AESTHETICS 2.16 JOHANNES KEPLER (1571–1630) AND POLYHEDRAL
NOMENCLATURE VERSUS COSMOLOGY 2.17 THE CHINESE ‘‘DEVIL’S
WORK BALLS’’ 2.18 BROOK TAYLOR (1685–1731) ON PERSPECTIVE
PROJECTION OF POLYHEDRA 2.19 MAX BRUCKNER (1860–1934) AND
HIS PAPER MODEL COLLECTION 2.20 ALEXANDER GRAHAM BELL
(1847–1922) AND INVENTIVE USE OF TETRAHEDRA 2.21 CONCLUSIONS 2.22 METHODOLOGY 2.23 ACKNOWLEDGMENTS 2.24 NOTES 2.25 INTRODUCTION 2.26 GOFF’S LEGACY 2.27 ACKNOWLEDGMENTS 2.28 NOTES 2.29 BIBLIOGRAPHY 3 Louis Kahn and Space Frames
3.1 INTRODUCTION 3.2 CONCLUSION 3.3 ACKNOWLEDGMENTS 3.4 NOTES 4 Buckminster Fuller and the Relevant Pattern
4.1 INTRODUCTION 4.2 THE RELEVANT PATTERN 4.3 NOTES 5 Polyhedral Structure
5.1 INTRODUCTION 5.2 AMERICAN EVANGELISM: IMPROVISED
RITUAL AND SPACE 5.3 THE REPRESENTAT8ON OF MORALITY:
THE CATHEDRAL AND THE HISTORICAL AVANT-GARDE 5.4 THE
GLASS CHAIN BORN AGAIN 5.5 FROM BOULLEE TO OLDENBURG:
THE STRUCTURE IN A POSTMODERN CONTEXT 5.6 THE
STRUCTURE AND AMERICAN MYTHOLOGIES OF NATURE 5.7 THE CONTEMPORARY PASTURE: A CATHEDRAL IN A PARK 5.8 CONCLUSION 5.9 NOTES 5.10 BIBLIOGRAPHY 6 Tetrahedral
Purity: The Javits Center
6.1 INTRODUCTION 6.2 ARCHITECTURE AND
POLITICS 6.3 6.4 CONCLUSION 6.5 BIBLIOGRAPHY 7 Double Curvature
Space Frames Supported on Four Points: Design and Construction of the
International Plaza of Portopia ‘81
7.1 INTRODUCTION 7.2 CONCLUSION 7.3 CONCLUSION 8 Deconstruction of the Cube
8.1 INTRODUCTION 8.2 THE REGULAR TETRAHEDRON AND OCTAHEDRON 8.3 THE
CUBOCTAHEDRON 8.4 THE STELLA OCTANGULA 8.5 CUBOCTAHEDRON
WITH CONSTITUENT TETRAHEDRA AND OCTAHEDRA 8.6 THE
RHOMBIC DODECAHEDRON 8.7 CONCLUSIONS 8.8 NOTES 9 The
Polyhedral World
9.1 INTRODUCTION 9.2 WHICH POLYHEDRA DO
WE KNOW? 9.3 NOTES 10 Proportion and Symbolism in Polyhedra
10.1 INTRODUCTION 10.2 CONCLUSION 10.3 SYMBOLISM AND
POLYHEDRA 10.4 The Constitution of Polyhedra and Their Interrelations 10.5 CONCLUSION 10.6 NOTES 11 The Structural Morphology of Basic
Polyhedra
11.1 INTRODUCTION 11.2 CONCLUSION 11.3 CONCLUSION 11.4 NOTES 12 Computer-Aided Processing of Polyhedric Configurations
12.1 INTRODUCTION 12.2 NOTES 13 Tensegrity: Theory and Application
13.1 INTRODUCTION 13.2 NOTES 14 Visual Morphology of Space Labyrinths:
A Source for Architecture and Design
14.1 INTRODUCTION 14.2 NOTES 15 Quasicrystal Architecture: The Space of Experience
15.1 INTRODUCTION 15.2 NOTES 16 Are Space Frames Habitable?
16.1 INTRODUCTION 16.2 INSIDE POLYHEDRA 16.3 16.4 THE HEXMOD: ITS MORPHOLOGY 16.5 CONCLUSION 16.6 NOTES 16.7 BIBLIOGRAPHY Index
2
3 Beyond the Cube
4
5 Beyond the Cube
6 The Architecture of
7 Space Frames and Polyhedra
8 J. Francois Gabriel
9 Editor
10
11 John Wiley & Sons, Inc.
12 NEW YORK / CHICHESTER / WEINHEIM / BRISBANE / SINGAPORE /
TORONTO
13 This text is printed on acid-free paper.
14 Copyright© 1997 by John Wiley & Sons, Inc.
15 All rights reserved. Published simultaneously in Canada.
16 Reproduction or translation of any part of this work beyond that permitted by Section 107 or
108 of the 1976 United States Copyright Act without the permission of the copyright owner is
unlawful. Requests for permission or further information should be addressed to the
Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY
10158–0012.
17 This publication is designed to provide accurate and authoritative information in regard to the
subject matter covered. It is sold with the understanding that the publisher is not engaged
in rendering legal, accounting, or other professional services. If legal advice or other
expert assistance is required, the services of a competent professional person should be
sought.
18 Library of Congress Cataloging-in-Publication Data
19 Beyond the cube : the architecture of space frames and polyhedra / J. Francois Gabriel,
editor.
20 p. cm.
21 Includes index.
22 ISBN 0–471–12261–0 (cloth : acid-free paper)
23
24 1. Space (Architecture) 2. Space frame structures. I. Gabriel, J. Francois, 1930-.
25 NA2765.B45 1997 97–3547
26 721' .042—dc21
27 Printed in the United States of America
28 Contents
29 Preface vii
30 J. Francois Gabriel, Syracuse University
31 Acknowledgments xiii
1.
Polyhedra, from Pythagoras to 32 Alexander Graham Bell 1
33 Jos Tomlow, Hochschule Zittau/Gorlitz, Germany
2.
Polyhedrality in the Architecture 34 of Bruce Goff. 35
35 Rollie Ristine
3.
Louis Kahn and Space Frames 127 36 Irene E. Ayad
4.
Buckminster Fuller and the Relevant Pattern 147 37 Arthur L. Loeb, Harvard University
5.
Philip Johnson’s Crystal Cathedral and the 38 Rhetoric of Its Free-Form Polyhedral Structure 161
39 Lawrence Davis, Syracuse University
6.
Tetrahedral Purity: The Javits Center 189 40 Matthys Levy
7.
Double Curvature Space Frames Supported 41 on Four Points: Design and Construction of the International Plaza of Portopia’81
211
42 Masao Saitoh, Nihon University
8.
Deconstruction of the Cube 229 43 Arthur L. Loeb, Harvard University
9.
The Polyhedral World 243 44 Pieter Huybers, Delft University of Technology
10.
Proportion and Symbolism in Polyhedra 281 45 Rene Motro, Universite de Montpellier
11.
The Structural Morphology of 46 Basic Polyhedra 301
47 Ture Wester, Royal Danish Academy of Fine Arts
12.
Computer-Aided Processing of 48 Polyhedric Configurations 343
49
50 Hoshyar Nooshin, with P. L. Disney and O. C. Champion, University of Surrey
13.
Tensegrity: Theory and Application 385 51 Ariel Hanaor, National Building Research Institute, Israel
14.
Visual Morphology of Space Labyrinths: 52 A Source for Architecture and Design 409
53 Haresh Lalvani, Pratt Institute
15.
Quasicrystal Architecture: 54 The Space of Experience 427
55 Tony Robbin
16.
Are Space Frames Habitable? 439 56 J. Francois Gabriel, Syracuse University
57 Contributors 495
58 Index 499
59
