Tetrahedral-dodecahedral honeycomb
Source đź“ť
180:
353:
344:
152:
143:
134:
369:
317:
27:
80:
57:
434:
418:
400:
253:
103:
263:
248:
113:
98:
90:
75:
67:
52:
258:
108:
268:
118:
85:
62:
449:
440:
424:
374:
391:
309:
313:
238:
184:
478:
276:
222:
179:
305:
352:
343:
34:
430:
414:
396:
234:
147:
421:(Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II, III, IV, V, p212-213)
321:
214:
151:
142:
133:
44:
406:
386:
472:
241:
191:
325:
297:
226:
138:
230:
129:
291:, so that there are no gaps. It is an example of the more general mathematical
284:
162:
210:
167:
403:. (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
15:
437:(Chapter 16-17: Geometries on Three-manifolds I, II)
456:, Ph.D. Dissertation, University of Toronto, 1966
328:to form a uniform honeycomb in spherical space.
304:Honeycombs are usually constructed in ordinary
463:, (2018) Chapter 13: Hyperbolic Coxeter groups
454:The Theory of Uniform Polytopes and Honeycombs
370:Convex uniform honeycombs in hyperbolic space
8:
18:
272:, and is named by its two regular cells.
335:
244:. It has a single-ring Coxeter diagram,
395:, 3rd. ed., Dover Publications, 1973.
411:The Beauty of Geometry: Twelve Essays
7:
203:Vertex-transitive, edge-transitive
19:Tetrahedral-dodecahedral honeycomb
312:. They may also be constructed in
219:tetrahedral-dodecahedral honeycomb
14:
351:
342:
266:
261:
256:
251:
246:
178:
150:
141:
132:
116:
111:
106:
101:
96:
88:
83:
78:
73:
65:
60:
55:
50:
428:The Shape of Space, 2nd edition
199:
190:
174:
158:
125:
43:
33:
23:
461:Geometries and Transformations
357:Centered on icosidodecahedron
1:
337:Wide-angle perspective views
318:hyperbolic uniform honeycombs
301:in any number of dimensions.
340:
413:, Dover Publications, 1999
39:{(5,3,3,3)} or {(3,3,3,5)}
495:
375:List of regular polytopes
348:Centered on dodecahedron
310:convex uniform honeycombs
308:("flat") space, like the
28:Compact uniform honeycomb
324:can be projected to its
287:or higher-dimensional
239:rhombitetratetrahedron
185:rhombitetratetrahedron
221:is a compact uniform
314:non-Euclidean spaces
338:
277:geometric honeycomb
225:, constructed from
336:
215:hyperbolic 3-space
444:Uniform Polytopes
392:Regular Polytopes
361:
360:
235:icosidodecahedron
207:
206:
486:
425:Jeffrey R. Weeks
355:
346:
339:
322:uniform polytope
271:
270:
269:
265:
264:
260:
259:
255:
254:
250:
249:
182:
154:
145:
136:
121:
120:
119:
115:
114:
110:
109:
105:
104:
100:
99:
93:
92:
91:
87:
86:
82:
81:
77:
76:
70:
69:
68:
64:
63:
59:
58:
54:
53:
16:
494:
493:
489:
488:
487:
485:
484:
483:
469:
468:
383:
366:
356:
347:
334:
267:
262:
257:
252:
247:
245:
183:
166:
146:
137:
117:
112:
107:
102:
97:
95:
89:
84:
79:
74:
72:
66:
61:
56:
51:
49:
45:Coxeter diagram
35:Schläfli symbol
12:
11:
5:
492:
490:
482:
481:
471:
470:
467:
466:
465:
464:
459:N.W. Johnson:
457:
441:Norman Johnson
438:
422:
404:
382:
379:
378:
377:
372:
365:
362:
359:
358:
349:
333:
330:
320:. Any finite
205:
204:
201:
197:
196:
194:
188:
187:
176:
172:
171:
160:
156:
155:
127:
123:
122:
47:
41:
40:
37:
31:
30:
25:
21:
20:
13:
10:
9:
6:
4:
3:
2:
491:
480:
477:
476:
474:
462:
458:
455:
451:
448:
447:
446:, Manuscript
445:
442:
439:
436:
435:0-8247-0709-5
432:
429:
426:
423:
420:
419:0-486-40919-8
416:
412:
408:
405:
402:
401:0-486-61480-8
398:
394:
393:
388:
385:
384:
380:
376:
373:
371:
368:
367:
363:
354:
350:
345:
341:
331:
329:
327:
323:
319:
315:
311:
307:
302:
300:
299:
294:
290:
286:
282:
281:space-filling
278:
273:
243:
242:vertex figure
240:
236:
232:
228:
224:
220:
216:
212:
202:
198:
195:
193:
192:Coxeter group
189:
186:
181:
177:
175:Vertex figure
173:
169:
164:
161:
157:
153:
149:
144:
140:
135:
131:
128:
124:
48:
46:
42:
38:
36:
32:
29:
26:
22:
17:
479:3-honeycombs
460:
453:
450:N.W. Johnson
443:
427:
410:
390:
326:circumsphere
303:
298:tessellation
296:
292:
288:
280:
274:
237:cells, in a
227:dodecahedron
218:
208:
231:tetrahedron
381:References
316:, such as
285:polyhedral
200:Properties
163:triangular
306:Euclidean
223:honeycomb
473:Category
364:See also
211:geometry
168:pentagon
407:Coxeter
387:Coxeter
209:In the
433:
417:
399:
332:Images
293:tiling
233:, and
217:, the
148:r{5,3}
289:cells
279:is a
159:Faces
139:{5,3}
130:{3,3}
126:Cells
431:ISBN
415:ISBN
397:ISBN
170:{5}
71:or
24:Type
295:or
283:of
213:of
165:{3}
94:or
475::
452::
409:,
389:,
275:A
229:,
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
↑
