64:
44:
474:
515:
242:
218:
332:
534:
508:
328:
140:
324:
91:
539:
501:
331:
sharing a common axis of rotational symmetry. It arises from superimposing two copies of the corresponding
63:
43:
302:
278:
445:
457:
453:
485:
203:
528:
335:(without rotational freedom), and rotating each copy by an equal and opposite angle.
423:
481:
449:
174:
262:
473:
362:
376:-gonal antiprisms (with rotational freedom), with symmetry group:
18:
436:
Skilling, John (1976), "Uniform
Compounds of Uniform Polyhedra",
438:
Mathematical
Proceedings of the Cambridge Philosophical Society
489:
338:This infinite family can be enumerated as follows:
509:
426:, sometimes not considered a true antiprism.
8:
21:
516:
502:
37:
323:Each member of this infinite family of
7:
470:
468:
346:>0 and for each rational number
14:
365:), there occurs the compound of 2
472:
333:prismatic compound of antiprisms
62:
42:
261:
202:
191:
180:
146:
124:
97:
87:
327:is a symmetric arrangement of
265:restricting to one constituent
1:
488:. You can help Knowledge by
325:uniform polyhedron compounds
556:
467:
342:For each positive integer
450:10.1017/S0305004100052440
354:>3/2 (expressed with
484:-related article is a
422:=2 the component is a
535:Polyhedral compounds
16:Polyhedral compound
33:-gonal antiprisms
497:
496:
321:
320:
279:improper rotation
83:
82:
547:
540:Polyhedron stubs
518:
511:
504:
476:
469:
460:
92:Uniform compound
66:
46:
39:
38:
19:
555:
554:
550:
549:
548:
546:
545:
544:
525:
524:
523:
522:
465:
435:
432:
402:
386:
313:
289:
253:
229:
118:
109:
17:
12:
11:
5:
553:
551:
543:
542:
537:
527:
526:
521:
520:
513:
506:
498:
495:
494:
477:
463:
462:
444:(3): 447–457,
431:
428:
412:
411:
410:
409:
397:
393:
381:
319:
318:
317:
316:
308:
292:
284:
266:
259:
258:
257:
256:
248:
232:
224:
206:
204:Symmetry group
200:
199:
193:
189:
188:
182:
178:
177:
148:
144:
143:
126:
122:
121:
120:
119:
116:
110:
107:
99:
95:
94:
89:
85:
84:
81:
80:
60:
35:
34:
15:
13:
10:
9:
6:
4:
3:
2:
552:
541:
538:
536:
533:
532:
530:
519:
514:
512:
507:
505:
500:
499:
493:
491:
487:
483:
478:
475:
471:
466:
459:
455:
451:
447:
443:
439:
434:
433:
429:
427:
425:
421:
417:
407:
403:
400:
394:
391:
387:
384:
378:
377:
375:
371:
368:
364:
361:
357:
353:
349:
345:
341:
340:
339:
336:
334:
330:
326:
314:
311:
304:
300:
296:
293:
290:
288:
280:
276:
272:
269:
268:
267:
264:
260:
254:
251:
244:
240:
236:
233:
230:
227:
220:
219:antiprismatic
216:
212:
209:
208:
207:
205:
201:
198:
194:
190:
187:
183:
179:
176:
173:
169:
165:
161:
157:
153:
149:
145:
142:
138:
134:
131:
127:
123:
114:
111:
105:
102:
101:
100:
96:
93:
90:
86:
78:
74:
70:
65:
61:
58:
54:
50:
45:
41:
40:
36:
32:
28:
25:
22:Compound of 2
20:
490:expanding it
479:
464:
441:
437:
419:
415:
413:
405:
398:
395:
389:
382:
379:
373:
369:
366:
359:
355:
351:
347:
343:
337:
322:
309:
306:
298:
294:
286:
282:
274:
270:
249:
246:
238:
234:
225:
222:
214:
210:
196:
185:
171:
167:
163:
159:
155:
151:
136:
132:
129:
112:
103:
76:
72:
68:
56:
52:
48:
30:
26:
23:
424:tetrahedron
529:Categories
482:polyhedron
430:References
329:antiprisms
162:} (unless
141:antiprisms
243:prismatic
175:triangles
125:Polyhedra
303:rotation
263:Subgroup
192:Vertices
115:even: UC
458:0397554
408:is even
363:coprime
139:-gonal
106:odd: UC
456:
414:Where
392:is odd
301:-fold
297:even:
277:-fold
273:odd: 2
241:-fold
237:even:
217:-fold
170:=2), 4
480:This
213:odd:
181:Edges
147:Faces
98:Index
486:stub
358:and
88:Type
79:=2)
75:=7,
71:=1,
59:=1)
55:=3,
51:=2,
446:doi
404:if
388:if
531::
454:MR
452:,
442:79
440:,
406:nq
399:np
390:nq
383:np
250:np
239:np
235:nq
226:np
215:np
211:nq
197:np
186:np
172:np
117:24
108:22
517:e
510:t
503:v
492:.
461:.
448::
420:q
418:/
416:p
401:h
396:D
385:d
380:D
374:q
372:/
370:p
367:n
360:q
356:p
352:q
350:/
348:p
344:n
315:)
312:h
310:p
307:C
305:(
299:p
295:q
291:)
287:p
285:2
283:S
281:(
275:p
271:q
255:)
252:h
247:D
245:(
231:)
228:d
223:D
221:(
195:4
184:8
168:q
166:/
164:p
160:q
158:/
156:p
154:{
152:n
150:4
137:q
135:/
133:p
130:n
128:2
113:q
104:q
77:q
73:p
69:n
67:(
57:q
53:p
49:n
47:(
31:q
29:/
27:p
24:n
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