Index
3 Abu Ali al-Hasan (Alhazen), 9
4 Adams (John Quincy) House (Vinita, Oklahoma, Goff), 69–70
5 Adath Jeshurun Synagogue and School Building (Elkins Park, Pennsylvania, Kahn), 136–137
6 Amman, Jost, 16, 18
7 Antiprisms:
89construction polyhedra, 262, 264–265
10 polyhedra, 253, 256–257, 259
11 Applewhite, E. J., 156, 157
12 Arabic world, polyhedra, 9, 154
13 Arch-grids, tensegrity, 393
14 Archimedes, 6
15 Archimedian polyhedra, computer-aided processing, 353–366.
16 See also Computer-aided processing Architecture:
1718geometry and, 427–438. See also Geometry
19habitability, 439–494. See also Habitability
20 Augmentation, construction polyhedra, 276–277
21 August of Saxony, 23
22 Ayad, Irene, ix
23 Baer, Steve, 434
24 Banchoff, Thomas, 432
25 Bank of China (Hong Kong, Pei), 466
26 Barbari, Jacopo de’, 12
27 Barbaro, Daniele, 11
28 Barbarossa Chandelier (Aachen Cathedral), 6–8
29 Bartlett, Jennifer, 183
30 Bartman (Irma) House (Triaero, Fem
31 Creek, Kentucky, Goff), 64–65, 68 Basic polyhedra. See also Computer-aided processing computer-aided processing, 344 defined, 302
32 Bass (William H.) House (Tulsa, Oklahoma, Goff), 59–64
33 Baursfeld, Walter, 330
34 Bell, Alexander Graham, viii, 28–30
35 Bernini, Gian, 168
36 Birkerts, Gunnar, 176
37 Black Bear Motor Lodge (Jackson
38 Hole, Wyoming, Goff), 71–72
39 Body ornaments, polyhedra, 2–3
40 Bone structure, 321, 323–324
41 Boullee, E.-L., 177
42 Bragdon, Claude, 38
43 Brahe, Tycho, 21
44 Briar Associates Projects (Bartlesville,
45 Oklahoma, Goff), 71
46 Bricard, R., 306
47 Brown, Denise Scott, 184
48 Bruckner, Max, 28, 250
49 Buckminsterfullerene, 158
50 Buffer forces, structural morphology, 309
51 Burgee, John, Crystal Cathedral
52 (Orange County, California, Johnson & Burgee), 161–187. See also
53 Crystal Cathedral (Orange County, California, Johnson 8c Burgee) Brut, M., 410, 419
54 Calladine, C. R., 399
55 Canting, computer-aided processing, 357
56 Case Study Movement, 176
57 Cauchy, Augustin-Louis, 303
58 Champion, O. C., xi
59 Choisy, Auguste, 132
60 Chorbachi, Wasma’a, 154 Chords. See Lattice structures Churchill, Winston, 58
61 City lower (Philadelphia, Pennsylvania,
62 Kahn), 130–135, 138–141
63 Civic Center-Forum (Philadelphia, Pennsylvania, Kahn), 141
64 Close packings, construction polyhedra, 262,263
65 COAST (Technical University, Denmark, Robbin), 437–438
66 Coccolithophores, 321, 323
67 Cole, Thomas, 181, 182
68 Collapse analysis, Javits Center (New
69 York City, Freed), 206–209 Complementary cap, hexmods, 450–451 Component tests, Javits Center (New
70 York City, Freed), 204
71 Computer-aided processing, 343–384 architectural objects, structural morphology, 319–320 basic polyhedra, 344 codes and P-names, 355–357 coordinate systems, 359, 362 face identity numbers and baselines, 362–366
7273generally, 353–355 geodesic configurations, 350–353 Goff, Bruce and, 40
74identity numbers and directions for edges, 369–372
75identity numbers and handles for vertices, 372–374
76 mapping
7778of edge-objects, 372 on edges, 347–349 of face-objects, 367–369 on faces, 345–347 of vertex-objects, 374 on vertices, 349–350
79multi-layer configurations, 378–380 ordering rules, 380–384 overview, 343–344
80Platonic and Archimedian polyhedra, 353–355
81polyhedric configurations, 353 polymation function, 374–377 properties, 358–359, 360–361 shaping and composing, 377–378
82 Connectivity, defined, 302 Connelly, Robert, 306
83 Construction polyhedra, 260–277 augmentation, 276–277 close packings, 262, 263 hemispherical structures, 265–272 prismatic and antiprismatic forms, 262, 264–265
84 prisms, 260
8586reciprocal sphere subdivisions, 272–276 solitary applications, 260–261
87 Cook, Peter, 467
88 Coordinate systems, computer-aided processing, 359, 362
89 Coxeter, H. S. M., 37,153,157,158, 281 Cret, Paul Philippe, 132 Critchlow, K., 9, 281, 297
90 Crystal Cathedral (Orange County, California, Johnson & Burgee), 161–187. See also Johnson, Philip contemporary pasture, 181–184 evangelism and, 163–167 glass chain, 171–177 morality, 167–171 nature and, 180–181 overview, 161–163, 185 postmodern context, 177–180
91 Crystal Chapel (Norman, Oklahoma, Goff), 90–102
92 Crystals. See Natural crystals Cube deconstruction, 229–241 cuboctahedron, 231–233, 234 duals, 239 overview, 229–230, 239–240 regular tetrahedron and octahedron, 230–231
9394rhombic dodecahedron, 237–239 Stella octangula, 233, 234, 235 truncated octahedron, 233, 235, 236, 237
95 Cubic form, 36 instability of, x, 466 prevalence of, vii proportion, 291–292
96 Cuboctahedron, 36 computer-aided processing, 344 cube deconstruction, 231–233, 234 described, 149–151 Fuller and, 153 Goff and, 92 habitability, 479, 481. See also Habitability
9798megapolyhedra, 468, 470 vector equilibrium, 153
99 Curved variants, space labyrinths, 419–425
100 Debussy, Claude, 40 Decks, habitability, 483
101 De Long, David, 43, 48, 56, 61, 89, 112
102 ‘‘Devil’s work ball’’ (Chinese), polyhe-dra, 25–27
103 Dipyramid (octahedron), 36, 69–70. See also Octahedron
104 Direct transformation, structural morphology, 312
105 Disney, P. L., xi
106 Dodecahedron, 36
107108computer-aided processing, 344 cube and, proportion, 291–292 history, 12, 13
109icosahedron and, proportion, 293 octahedron and, proportion, 292 rhombic, cube deconstruction, 237–239
110 tetrahedron and, proportion, 292 Doors, habitability, 443, 483 Doppelmayr, J. G., 23
111 Double-layer tensegrity grids, 393–395, 398, 400, 401. See also Tensegrity
112 Dualism, defined, 304
113 Duality:
114115computer-aided processing, 357 defined, 304
116 Dual objects:
117118cube deconstruction, 239 defined, 304
119 Dual structures:
120121geometrical qualities of, 314–315 structural qualities of, 315–316
122 Dual transformation, defined, 304 Diirer, Albrecht, 11, 14–16, 16 Dynamic relaxation method, tensegrity, load response, 400
123 Eames, Charles, 176
124 Eames, Ray, 176
125 Echinodermata, 321, 326
126 Edmondson, Amy, 157
127 Eiffel, Gustave, 466
128 Elements, defined, 302
129 Elevators, hexmods, 446,475
130 Emmerich, D. G., 277, 386, 391,396, 397
131 Equilibrium forces, structural morphology, 310–311
132 Escher, M. C., 154, 155 Euclid, 1, 3, 5, 9, 14, 16, 25 Euler, L., 304
133 Evangelism, 163–167
134 Face mapping. See Mapping Faust, Robert, 65, 67, 68 Fire safety, hexmods, 453, 475–476 First National Bank (Independence, Missouri, Goff), 77–81
135 Flexibility, defined, 305
136 Floor plans:
137138habitability, 486–488 tessellated, 48
139 Floors, habitability, 484
140 Floral Hills Temple of Rest (Las Vegas Nevada, Goff), 51
141 Foraminifera (plankton), 321, 322 Ford, Henry, vii
142 Formalism, rejection of, 43
143 Formex algebra, computer-aided processing, 343
144 Foster, Norman, 176
145 Fourth dimension, geometry, 430–433 Frampton, Kenneth, 171, 176
146 Freed, James Ingo, 189–209. See also Javits Convention and Exhibition Center (NYC, Pei, Cobb, and Freed)
147 Frustum, 36
148 Fuller, Anne Hewlett, 157
149 Fuller, Margaret, 156
150 Fuller, R. Buckminster, ix, xi, 37, 46, 80, 101, 104, 127, 129, 130, 133, 147–159, 232, 306, 330, 332, 385–390, 391, 396, 467
151 Gabriel, J. Frangois, 31, 337
152 Garden Grove Community Chapel. See Crystal Cathedral (Orange County, California, Johnson & Burgee)
153 Gaudf, Antonio, 31, 37, 39, 98
154 Gaussian curvature:
155 defined, 304
156157dual structures, geometrical qualities of, 314–315
158 Gehry, Frank, 40
159 Geodesic configurations, computer-aided processing, 350–353
160 Geodesic domes, 36, 46, 391. See also
161 Tensegrity
162 Geometric rigidity, tensegrity, load response, 399–400
163 Geometry, 427–438
164165architectural space and, 427–430 fourth dimension, 430–433 quasicrystals, 433–438
166 tensegrity, 390–398. See also Tensegrity
167 Ghyka, M. C., 281, 284
168 Gillespie, John Burkes, 97
169 Glass chain, Crystal Cathedral (Orange
170 County, California, Johnson &
171 Burgee), 171–177
172 Goff, Bruce, viii, 35–126
173 architectural history and, 38–39
174 computer and, 40
175 geometry and, 40–42, 44
176 legacy of, 118–119
177 monumentality, 42–43
178 overview, 35–36
179 polyhedra and, 36–38, 44–46, 48–50
180181psychology and symbolism, 42 spatial experience and, 43 works, 50–118
182Adams (John Quincy) House (Vinita, Oklahoma), 69–70
183Bartman (Irma) House (Triaero, Fem Creek, Kentucky), 64–65, 68
184Bass (William H.) House (Tulsa, Oklahoma), 59–64
185Black Bear Motor Lodge (Jackson Hole, Wyoming), 71–72
186Briar Associates Projects (Bartlesville, Oklahoma), 71
187Crystal Chapel (Norman, Oklahoma), 90–102
188First National Bank (Independence, Missouri), 77–81
189Floral Hills Temple of Rest (Las Vegas Nevada), 51
190Gutman (Emil) House (Gulfport, Mississippi), 65–68
191Hyde/Lane (Lawrence and Scott) House (Kansas City, Missouri), 50–51
192Jones (Howard) House (Bartlesville, Oklahoma), 81–82
193MacBryde (W. R.) House (Kansas City, Kansas), 73–74
194Nicol (Mr. and Mrs. James) House (Kansas City, Missouri), 51–59
195Phi Beta Delta Fraternity House (Norman, Oklahoma), 75
196Phi Sigma Epsilon Fraternity House (Talequah, Oklahoma), 73
197Pi Lambda Phi Fraternity House (Norman, Oklahoma), 75–77
198Pollock/Warriner (Donald, John, and Laura) House (Oklahoma City, Oklahoma), 111–118
199Price (Joe) Studio and Residence (Bartlesville, Oklahoma), 82–90
200Rudd (Vernon E.) House (San Mateo, California, 102–105
201Snyder (Russell B.) House, 47 Unseth/Newman (Helen and
202Sheldon) House (Park Ridge, Illinois), 70–71
203 Wilson (James D.) House (Pensacola, Florida), 105–111 Golden proportion, 43, 282–288 Graham, Billy, 165, 166, 169 Grantham, Larry Wayne, 44, 80, 81, 86, 110
204 Greek antiquity: polygons, 3–4 polyhedra, 5–6
205 Greene, Herb, 35, 40–42 Grip, R., 396
206 Gropius, Walter, 135
207 Gunn, Charles, 412
208 Gutman (Emil) House (Gulfport, Mississippi, Goff), 65–68
209 Habitability, 439–494
210 hexmods, 447–459
211 building system, 453–459
212 generally, 447–452
213214lattice structures, 444–447 overview, 439–440, 490–492 polyhedra interiors, 440–444
215space frames and polyhedra, 476–481
216space trusses and megapolyhedra, 466–476
217 star beam, 459–466
218 unadulterated polyhedra, 481–490
219 Haeckel, E. H.P.A., 31
220 Hanaor, Ariel, xii
221 Harrison, Wallace, 95
222 Harvey, David, 170, 171, 173
223 Haughton, Eric, 155
224 Hayden, Hans, 18
225 Heath, James, 97
226 Helicoidal module, hexmods, 454, 473, 474, 475
227 Hemispherical structures, construction polyhedra, 265–272
228 Hexagon, habitability, 466
229 Hexmods, 447–459
230 building system, 453–459
231 generally, 447–452
232 habitability, 466
233 large buildings, 473–476
234 star beam compared, 459, 460–461
235 Hilbert, D., 281
236 Hockney, David, 183
237 Holden, Alan, 442
238 Honeycomb pattern, 448, 466
239 Huybers, Pieter, x
240 Hyde/Lane (Lawrence and Scott)
241242House (Kansas City, Missouri, Goff), 50–51
243 Hyper-polyhedra, tensegrity, 396
244 Icosahedron, 36 computer-aided processing, 344 dodecahedron and, proportion, 293
245 Icosidodecahedron, 36, 309
246 Imperfect polyhedra, 37
247 Inness, George, 181
248 International Plaza of PORTOPIA’81 (Kobe, Japan). See PORTOPIA’81 (Kobe, Japan)
249 Islam. See Arabic world
250 Jamnitzer, Wenzel, 16–20
251 Javits Convention and Exhibition Center (NYC, Pei, Cobb, and Freed), x, 189–209
252253assembly, 197–199
254collapse analysis, 206–209 component tests, 204
255fabrication and construction, 201–204 geometry and structural form, 190–194
256jointing, 194–197 overview, 189 politics and, 189–190 risk models, 204–205
257structural analysis, 199–200 ultimate load capacity, 206
258 Jeanneret, Pierre, 167
259 Jewish Community Center/Day Camp (Trenton, New Jersey, Kahn), 138
260 John Hancock Tower (Chicago, Illinois, Khan), 466
261 Johnson, Philip, ix-x, 40, 101, 102, 161–187. See also Crystal Cathedral (Orange County, California, Johnson & Burgee)
262 Jointing, Javits Center (NYC, Pei, Cobb, and Freed), 194–197
263 Jones (Howard) House (Bartlesville, Oklahoma, Goft), 81–82
264 Kahn, Louis I., ix, 127–146, 175, 467 Adath Jeshurun Synagogue and
265266School Building (Elkins Park, Pennsylvania), 136–137
267City Tower (Philadelphia, Pennsylvania), 130–135, 138–141
268Civic Center-Forum (Philadelphia, Pennsylvania), 141
269 Jewish Community Center/Day
270271Camp (Trenton, New Jersey), 138 overview, 127–128
272Yale University Art Gallery (New Haven, Connecticut), 128–130, 135–136
273 Kent, George, 175
274 Kepes, Gyorgy, 157
275 Kepes, Juliette, 157
276 Kepler, Johannes, 4, 9, 12, 21–22, 257, 301
277 Khan, Fazlur, 466
278 Kindi, A1-, 9
279 Kites, polyhedra and, 28
280 Knoppe, Hugo, 24, 25
281 Koller, Christof, 24
282 Laban, Rudolf von, 229
283 Lalvani, Haresh, xii, 281, 298, 410, 421,424,433
284 Langer, Suzanne, K., 42
285 Large buildings, space trusses and megapolyhedra, 466–467
286 Lattice structures:
287288combined lattice and plate structures, structural morphology, 337–340
289 defined, 303
290 habitability, 442, 444–447. See also
291 Habitability
292293structural morphology, man-made structures, 330
294 tetrahedron, history of, 28
295 Lautner, John, 102
296 Lawlor, R., 281
297 Le Corbusier, ix, 43, 75, 83, 142, 167, 168,281,453
298 Ledoux, C.-N., 177
299 Lencker, Hans, 18, 20, 24
300 Le Ricolais, Robert, 127, 133, 134 Levy, Matthys, x
301 Levy, R., 400
302 Lichtenstein, Roy, 180
303 Links and linking, defined, 302
304 Livability. See Habitability
305 Load response, tensegrity, 399–405.
306 See also Tensegrity
307 Lobenigk, Egidius, 24
308 Loeb, Arthur L., x, 147–159
309 London Zoo aviary, 386, 387
310 Lower cap, hexmods, 449, 450–451
311 Lyotard, Jean-Frangois, 173
312 MacBryde (W. R.) House (Kansas City,
313 Kansas, Goff), 73–74
314 Maggiore, Giovanni Ambrogio, 24
315 Mainestone, R., 13
316 Malkevitch, J., 6
317 Mapping:
318319of edge-objects, computer-aided processing, 372
320on edges, computer-aided processing, 347–349
321of face-objects, computer-aided processing, 367–369
322on faces, computer-aided processing, 345–347
323of vertex-objects, computer-aided processing, 374
324on vertices, computer-aided processing, 349–350
325 Marx, Leo, 180
326 Maxwell, Delle, 412
327 Mazzocchio (hat), 9–11
328 Medieval forms, polyhedra, 6–8
329 Megapolyhedra, habitability, 466–476
330 Metamorphology, systematic, space labyrinths, 411–415
331 Meton, 282
332 Metric geometry, defined, 302
333 Meurant, R. C., 281
334 Michelangelo, 13
335 Mies vander Rohe, Ludwig, ix, 43, 83, 140, 142, 167, 171
336 Miyazaki, Koji, 424, 433, 434
337 Mobius, August Ferdinand, 303, 304–305, 306, 308, 340
338 Mobius strip, 303
339 Mobius’ theorem, 304, 307
340 Modeling, architectural objects, structural morphology, 317–320
341 Monumental! ty, polyhedra, 42–43
342 Moody, D. L., 165, 166
343 Morality, Crystal Cathedral (Orange
344345County, California, Johnson & Burgee), 167–171
346 Morris, William, 181
347 Motro, Rene, xi, 355, 395
348 Movability, defined, 305
349 Muller, John, 173, 175
350 Multicell regular polyhedra, Goff, Bruce, 46, 48
351 Multi-layer configurations, computer-aided processing, 378–380
352 Natural crystals: ordering of, 151–152 polyhedra, 1–2, 36
353 X-ray diffraction patterns, 158
354 Natural plate and lattice structures, 320–327
355356bone structures, 321, 323–324 generally, 320–322
357planktonic organisms, 321, 322, 323 sea urchin, 325–327
358 Venus’s-flower-basket, 321, 324–325
359 Nature, Crystal Cathedral (Orange County, California, Johnson & Burgee), 180–181
360 Networks, tensegrity, 393–395
361 Neudorfer, Johann, 16
362 Neufchatel, Nicolas, 16
363 Neutra, Richard, 169, 176, 179
364 Neutrality, defined, 305
365 Nicol (Mr. and Mrs. James) House (Kansas City, Missouri, Goff), 51–59
366 Nielsen, J., 306
367 Nonregular polyhedra, Goff, Bruce, 45–46
368 Nooshin, Hoshyar, xi
369 Oblique walls, habitability, 476, 483 Octagons, Goff, Bruce, 52–59, 81–82 Octahedral stelladon, Goff, Bruce, 95–96
370 Octahedron, 36
371372computer-aided processing, 344 dodecahedron and, proportion, 292 Goff, Bruce, 69–70
373 interiors of, habitability, 441. See also
374375Habitability megapolyhedra, 468, 469 natural crystals, 151–152 regular, cube deconstruction, 230–231 truncated, cube deconstruction, 233, 235,236,237
376 Ogawa, T., 435
377 Oldenberg, Claes, 180
378 Otto, Frei, 423
379 Pacioli, Luca, 11–13, 28, 281, 290, 298 Paper models, polyhedra, 28, 29 Pappus, 6
380 Parabola, pure plate structures, structural morphology, 335–336
381 Parallelpiped architectural spaces, ubiquity of, 43
382 Park, Ben Allan, 38
383 Pastoral metaphor, Crystal Cathedral
384385(Orange County, California, Johnson & Burgee), 180–181
386 Paxton, Joseph, 97, 176
387 Pearce, Peter, 156, 298, 410, 419 Pei, Cobb, and Freed, x
388 Pei, I. M., 102, 466
389 Pellegrino, S., 399
390 Pelli, Cesar, 176
391 Pentagon, golden proportion, 282–288 Pentagonal geometry, Goff, Bruce, 61–64 Perspective projection, polyhedra, 27 Pfinzing, Paulus, 18
392 Phi Beta Delta Fraternity House (Norman, Oklahoma, Goff), 75
393 Phidias of Cercio, 13
394 Phi Sigma Epsilon Fraternity House (Talequah, Oklahoma, Goff), 73
395 Phisterer, Henry A., 128
396 Piero della Francesca, 11, 12
397 Pi Lambda Phi Fraternity House (Norman, Oklahoma, Goff), 75–77
398 Planing, computer-aided processing, 357
399 Planktonic organisms, 321, 322, 323
400 Plate structures:
401402combined lattice and plate structures, structural
403morphology, 337–340 defined, 303
404structural morphology, man-made structures, 330–337
405 Plato, xi, 5, 6, 281, 289, 290, 295, 296–298, 301
406 Platonic polyhedra, computer-aided processing, 353–356. See also Computer-aided processing
407 Poincare, J.-H., 424, 430
408 Polar reciprocation, structural morphology, 311–312
409 Politics, Javits Center (NYC, Pei, Cobb, and Freed), 189–190
410 Pollock/Warriner (Donald, John, and Laura) House (Oklahoma City, Oklahoma, Goff), 111–118
411 Polo, Marco, 25
412 Polygonal subdivisions, construction polyhedra, 268–272
413 Polygons:
414 Arabic world, 9
415 Greek antiquity, 3–4
416 Polyhedra, 243–279
417 classes of, 36
418 computer-aided processing, 343–384.
419420See also Computer-aided processing construction, 260–277. See also Con
421 struction polyhedra
422423definitions, 36, 245, 302, 303, 304, 305
424Goff, Bruce, 35–126. See also Goff, Bruce
425golden mean ratio, 43 history of, 1–34
426Arabic contributions, 9 Bell, Alexander Graham, 28–30 body ornaments, 2–3 Bruckner, Max, 28
427Chinese ‘‘devil’s work ball,’’ 25–27 Diirer, Albrecht, 14–16 Greek antiquity, 3–6 Jamnitzer, Wenzel, 16–21 Kepler, Johannes, 21–22 Medieval forms, 6–8 natural crystals, 1–2 Neudorfer, Johann, 16 Pacioli, Luca, 11–13 Piero della Francesca, 11 Taylor, Brook, 27 Uccello, Paolo, 9–11 Vinci, Leonardo da, 13–14 Zick, Lorenz, 22–25
428imperfect, 37 interiors of, habitability, 440–444.
429See also Habitability monumentality, 42–43 overview, 243 prisms and antiprisms, 253, 256–257, 259
430proportion and, 282–294. See also Proportion
431psychology and symbolism, 42 reciprocal faces, 250, 252–253, 254, 255
432reciprocals, 250 regular forms, 36 stellated (Kepler-Poinsot) polyhedra, 257–258, 260
433structural morphology, 301–342. See also Structural morphology symbolism, 294–298
434essence of, 295–296 generally, 294–295 Plato’s cosmogony, 296–298 tensegrity, 390–393. See also Tensegrity types of, 245–249 vertex situations, 249–250
435 Polyhedral sphere subdivisions, construction polyhedra, 267
436 Polyhedric configuration: computer-aided processing, 353 defined, 343
437 Polymation function, computer-aided processing, 374–377
438 PORTOPIA’81 (Kobe, Japan), 211–227 construction, 223–225, 226 overview, 211–213, 225, 227 space truss shell numerical analysis, 221–222
439440structural design, 222–223 structural outline, 213–215 structural planning, 215–221
441curved surface transition, 218–219 form, 216–218
442 member arrangement, 219–221 Postmodern context, Crystal Cathedral
443444(Orange County, California, Johnson & Burgee), 177–180
445 Price, Joe, 40
446 Price (Joe) Studio and Residence (Bartlesville, Oklahoma, Gofi), 82–90
447 Prisms, 36 construction polyhedra, 260, 262, 264–265
448449Goff, Bruce, 45–46 polyhedra, 253, 256–257, 259 skew prism, tensegrity, 390–391
450 Proportion, 282–294 golden, 282–288 overview, 281, 282 polyhedra, 288–294 dodecahedron and cube, 291–292 dodecahedron and icosahedron, 293 dodecahedron and octahedron, 292 dodecahedron and tetrahedron, 292 generally, 288–290 spheres, 293–294
451 Proust, Marcel, 43
452 Psychology, polyhedra, 42
453 Pure lattice structures, structural morphology, man-made structures, 330
454 Pure plate structures, structural morphology, man-made structures, 330–337
455 Pyramidization, construction polyhedra, 265–267
456 Pyramids, 36, 78 Pythagoras, viii, 1, 3
457 Quarter-tetrahedron, cube deconstruction, 238, 239
458 Quasicrystals, 158, 433–438. See also Geometry
459 Radiolaria (plankton), 321, 322
460 Reciprocal faces, polyhedra, 250, 252–253, 254, 255
461 Reciprocals, polyhedra, 250
462 Reciprocal sphere subdivisions, construction polyhedra, 272–276
463 Redundancy, defined, 305
464 Regular octahedron, cube deconstruction, 230–231
465 Regular polyhedra, described, 36
466 Regular tetrahedron, cube deconstruction, 230–231
467 Renaissance, polyhedra, 9, 11, 14, 16–21
468 Revivalism, Crystal Cathedral (Orange
469470County, California, Johnson & Burgee), 163–167
471 Rhombic dodecahedron, cube deconstruction, 237–239
472 Rhombic hexahedron, Goff, Bruce, 96–97
473 Rhombic triacontahedron, structural morphology, 309
474 Rhombicuboctahedron, history, 12 Rigidity:
475 defined, 305
476477geometric, tensegrity, load response, 399–400
478 man-made structures, 328–330
479 Risk models, Javits Center (New York City, Freed), 204–205
480 Ristine, Rollie, viii
481 Robbins, Tony, xii
482 Roche, Kevin, 176
483 Rodgers, Richard, 176
484 Room height, habitability, 440
485 Rowe, Peter, 166, 180, 181, 182, 183 Rudd (Vernon E.) House (San Mateo,
486 California, Goff), 102–105
487 Ruskin, John, 181
488 Saarinen, Eero, 176
489 Sadao, Shoji, 101, 154
490 Safdie, Moshe, 102, 158
491 Saitoh, Masao, x
492 Satie, Erik, 40
493 Scheerbart, Paul, 171
494 Schindler, Rudolf, 176
495 Schoen, A., 410
496 Schuller, Robert, 165, 166, 167, 168,
497 169, 170, 171, 173, 179
498 Schwedler, J. W., 330, 332
499 Sea urchin, 321, 325–327
500 Sensitivity, defined, 305
501 Sergeant, John, 64
502 Shear force, defined, 303
503 Simple polyhedra, defined, 302 Single-cell regular polyhedra, Goff,
504 Bruce, 46
505 Single-layer tensegrity grids, 395 Skew prism, tensegrity, 390–391 Skidmore, Owings, and Merrill, 99 Skinner, B. E, 155
506 Slack, Rex, 110
507 Snelson, Kenneth, 387, 388, 389
508 Snubbing, computer-aided processing, 357
509 Snyder (Russell B.) House (Goff), 47 Space frames, polyhedra and, habitabil
510 ity, 476–481
511 Space labyrinths, 409–426
512513curved variants and derivatives, 419–425
514 generation, 415–418
515 overview, 409–411
516 systematic metamorphology, 411–415 Space lattice. See Lattice structures Space trusses, habitability, 466–476 Space truss shell numerical analysis,
517518PORTOPIA’81 (Kobe, Japan), 221–222
519 Spheres, proportion, 293–294
520 Spider webs, 321
521 Spillers, W. R., 400
522 Spinel, 147–148
523 Stability, defined, 305
524 Staircase:
525 hexmods, 453–456
526 lattice structures, 446
527 Star beam, habitability, 459–466
528 Stella octangula, cube deconstruction, 233,234,235
529 Stellated (Kepler-Poinsot) polyhedra, 257–258, 260
530 Stevin, Simon, 277
531 Stiffness method, tensegrity, load response, 400
532 Stone, Barton Warren, 166
533 Storer, Lorenz, 18, 21
534 Structural analysis, Javits Center (New York City, Freed), 199–200
535 Structural design, PORTOPIA’81 (Kobe, Japan), 222–223
536 Structural morphology, 301–342 architectural objects, 316–320 modeling structures, 317–320 plate action, 320 visually-based analysis and design, 316–317
537538definitions, 302, 303, 304, 305 dual structures
539geometrical qualities of, 314–315 structural qualities of, 315–316 historical perspective, 303–314 man-made structures, 327–340
540combined lattice and plate structures, 337–340
541generally, 327–328 pure lattice structures, 330 pure plate structures, 330–337 rigidity, 328–330
542natural plate and lattice structures, 320–327
543bone structures, 321, 323–324 generally, 320–322
544planktonic organisms, 321, 322, 323
545 sea urchin, 325–327
546547Venus’s-flower-basket, 321, 324–325
548 overview, 301–303, 340–341 Structural outline, PORTOPIA’81
549 (Kobe, Japan), 213–215. See also
550 PORTOPIA’81 (Kobe, Japan) Structural planning, PORTOPIA’81
551 (Kobe, Japan), 215–221. See also
552 PORTOPIA’81 (Kobe, Japan)
553 Sullivan, Louis, 48
554 Sunday, Billy, 165, 166
555 Symbolism, 294–298
556557essence of, 295–296 generally, 294–295
558Plato’s cosmogony, 296–298 polyhedra, 42
559 Systematic metamorphology, space
560 labyrinths, 411–415
561 Tafiiri, Manfredo, 179
562 Tall buildings, space trusses and megapolyhedra, 466–467
563 Tatlin, Vladimir, 167
564 Taut, Bruno, 97, 171
565 Taut, Max, 97
566 Taylor, Brook, 27
567 Technology:
568569Crystal Cathedral (Orange County, California, Johnson & Burgee), 177, 179
570 hexmods, 452
571 Tensegrity, xi-xii, 385–408
572 assessment, 405–407
573 definitions, 385–386
574 geometry, 390–398
575 networks, 393–395
576 polyhedra, 390–393
577578structural forms, 395–398 historical perspective, 386–390 load response, 399–405
579characteristics of, 400–405 geometric rigidity, 399–400 structural analysis, 400
580 Tessellated floor plan, 48
581 Tetrahedron, 36 computer-aided processing, 344 dodecahedron and, proportion, 292 Goff, Bruce, 71–72, 92 history of, 28, 30–31
582583interiors of, habitability, 441. See also Habitability
584Kahn, Louis L, 128 megapolyhedra, 468 natural crystals, 151–152 quarter-tetrahedron, cube deconstruction, 238, 239
585 regular, cube deconstruction, 230–231 Thomson, D’Arcy Wentworth, 131 Thurston, William, 412
586 Timaeus, 5, 289
587 Timoshenko, Stephen P., 306
588 Tomlow, Jos, viii
589 Topological information, defined, 302
590 Transformation, structural morphology, 312–313
591 Triacontahedron, rhombic, structural morphology, 309
592 Triaero (Irma Bartman House, Fem Creek, Kentucky, Goff), 64–65, 68
593 Triangular design, Goff, Bruce, 65–69 Truncated octahedron:
594595cube deconstruction, 233, 235, 236, 237
596habitability, 479, 481. See also Habitability
597 megapolyhedra, 468, 469
598 Truncated tetrahedron: habitability, 479, 481. See also Habitability
599 megapolyhedra, 468, 469, 470
600 Truncation:
601602computer-aided processing, 357 construction polyhedra, 275–276
603 Tyng, Anne Griswold, ix, 127, 129, 130, 131, 133, 138, 140, 411,467
604 Uccello, Paolo, 9–11
605 Ultimate load capacity, Javits Center (New York City, Freed), 206
606 Unit cell, 148
607 Unseth/Newman (Helen and Sheldon) House (Park Ridge, Illinois, Goff), 70–71
608 Upper cap, hexmods, 449, 450–451
609 Valency, defined, 302 van der Ende, Gerrit, 277 van Gogh, Vincent, 430 Varney, William, 153–154
610 Vasari, Giorgio, 9, 13
611 Vector equilibrium, 149, 153, 232
612 Venturi, Robert, 184 Venus’s-flower-basket, 321, 324–325 Vertex situations, polyhedra, 249–250 Vieus, M., 295
613 Vilnay, O., 396, 397
614 Vinci, Leonardo da, 12, 13–14
615 Viollet-Le-Duc, Emmanuel, 132, 167 Virtual polyhedra, Goff, Bruce, 44–45 Visual morphology, of space labyrinths, 409–426. See also Space labyrinths
616 Wainwright, William, 152
617 Walls:
618619glazed, habitability, 484–485 oblique, habitability, 476, 483
620 Warhol, Andy, 180
621 Wecker, Georg, 24
622 Wester, Ture, xi
623 Wilson (James D.) House (Pensacola, Florida, Goff), 105–111
624 Windows, habitability, 483, 484–485 Wood, Robert, 166
625 Wright, Frank Lloyd, ix, 37, 45, 68, 75, 76, 78, 82, 83, 86, 87, 98, 99, 108, 118, 142,440, 456, 466
626 Yale University Art Gallery (New Haven, Connecticut, Kahn), 128–130, 135–136
627 Zick, Lorenz, 22–25, 26