187:
209:
320:
307:
40:
363:
296:
331:
1007:
495:, each extending in both directions to the same vertex at infinity, in order to maintain symmetry. In practice, the model prisms are cut off at a certain point that is convenient for the maker. Wenninger suggested these figures are members of a new class of
693:
1048:
686:
503:. However, he also suggested that strictly speaking, they are not polyhedra because their construction does not conform to the usual definitions.
793:
604:
162:
679:
100:
911:
896:
881:
798:
410:
129:
105:
95:
926:
901:
886:
110:
921:
916:
876:
155:
710:
1041:
906:
843:
833:
773:
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733:
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230:
848:
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311:
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519:
143:
1034:
986:
981:
768:
461:
175:
783:
778:
429:
50:
891:
480:
527:- The ten vertices at infinity correspond directionally to the 10 vertices of this abstract polyhedron.
186:
388:
57:
196:
818:
828:
823:
758:
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457:
424:
300:
281:
148:
633:
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476:
335:
273:
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319:
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208:
39:
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702:
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472:
468:
439:
373:
362:
87:
17:
1018:
810:
257:
119:
1061:
250:
246:
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295:
339:
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269:
666:
1014:
496:
596:
657:
638:
671:
238:
218:
1006:
242:
456:
is the dual of the great dodecahemicosahedron, and is one of nine
206:
675:
260:
with ten hexagonal faces passing through the model center.
506:
The great dodecahemicosahedron can be seen as having ten
1022:
284:(having the pentagonal faces in common), and with the
290:
29:
935:
867:
807:
747:
709:
1042:
687:
618:(Page 101, Duals of the (nine) hemipolyhedra)
8:
1049:
1035:
694:
680:
672:
460:. It appears visually indistinct from the
564:
491:, they are represented with intersecting
352:
288:(having the hexagonal faces in common).
213:3D model of a great dodecahemicosahedron
537:
794:nonconvex great rhombicosidodecahedron
7:
1003:
1001:
245:), 60 edges, and 30 vertices. Its
25:
912:great stellapentakis dodecahedron
897:medial pentagonal hexecontahedron
882:small stellapentakis dodecahedron
799:great truncated icosidodecahedron
124:5/4 5 | 3 (double covering)
1005:
927:great pentagonal hexecontahedron
902:medial disdyakis triacontahedron
887:medial deltoidal hexecontahedron
547:"65: great dodecahemicosahedron"
471:passing through the center, the
361:
329:
318:
305:
294:
185:
108:
103:
98:
93:
38:
922:great disdyakis triacontahedron
917:great deltoidal hexecontahedron
877:medial rhombic triacontahedron
479:at infinity; properly, on the
1:
907:great rhombic triacontahedron
467:Since the hemipolyhedra have
1021:. You can help Knowledge by
844:great dodecahemidodecahedron
834:small dodecahemidodecahedron
774:truncated dodecadodecahedron
764:truncated great dodecahedron
734:great stellated dodecahedron
724:small stellated dodecahedron
634:"Great dodecahemicosahedron"
328:
317:
304:
293:
231:nonconvex uniform polyhedron
849:great icosihemidodecahedron
839:small icosihemidodecahedron
789:truncated great icosahedron
667:Uniform polyhedra and duals
227:great dodecahemiicosahedron
33:Great dodecahemicosahedron
1089:
1000:
972:great dodecahemidodecacron
962:small dodecahemidodecacron
859:small dodecahemicosahedron
854:great dodecahemicosahedron
653:"Great dodecahemicosacron"
589:Cambridge University Press
445:Great dodecahemicosahedron
325:Great dodecahemicosahedron
312:Small dodecahemicosahedron
286:small dodecahemicosahedron
223:great dodecahemicosahedron
977:great icosihemidodecacron
967:small icosihemidodecacron
520:List of uniform polyhedra
360:
356:Great dodecahemicosacron
355:
37:
32:
987:small dodecahemicosacron
982:great dodecahemicosacron
769:rhombidodecadodecahedron
703:Star-polyhedra navigator
597:10.1017/CBO9780511569371
462:small dodecahemicosacron
454:great dodecahemicosacron
349:Great dodecahemicosacron
176:Great dodecahemicosacron
27:Polyhedron with 22 faces
18:Great dodecahemicosacron
784:great icosidodecahedron
779:snub dodecadodecahedron
51:Uniform star polyhedron
1017:-related article is a
938:uniform polyhedra with
892:small rhombidodecacron
501:stellation to infinity
237:. It has 22 faces (12
214:
481:real projective plane
276:. It also shares its
251:crossed quadrilateral
212:
940:infinite stellations
748:Uniform truncations
405:= 22 (χ = −8)
74:= 30 (χ = −8)
868:Duals of nonconvex
819:tetrahemihexahedron
475:have corresponding
936:Duals of nonconvex
829:octahemioctahedron
824:cubohemioctahedron
808:Nonconvex uniform
759:dodecadodecahedron
750:of Kepler-Poinsot
729:great dodecahedron
717:regular polyhedra)
650:Weisstein, Eric W.
631:Weisstein, Eric W.
458:dual hemipolyhedra
301:Dodecadodecahedron
282:dodecadodecahedron
215:
114:(double covering)
1068:Uniform polyhedra
1030:
1029:
995:
994:
947:tetrahemihexacron
870:uniform polyhedra
739:great icosahedron
606:978-0-521-54325-5
581:Wenninger, Magnus
450:
449:
346:
345:
336:Icosidodecahedron
274:icosidodecahedron
264:Related polyhedra
205:
204:
16:(Redirected from
1080:
1073:Polyhedron stubs
1051:
1044:
1037:
1009:
1002:
957:octahemioctacron
952:hexahemioctacron
696:
689:
682:
673:
663:
662:
644:
643:
617:
572:
561:
555:
554:
542:
525:Hemi-icosahedron
499:figures, called
485:Magnus Wenninger
483:at infinity. In
425:Index references
365:
353:
333:
322:
309:
298:
291:
278:edge arrangement
211:
189:
144:Index references
113:
112:
111:
107:
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102:
101:
97:
96:
42:
30:
21:
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939:
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869:
863:
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711:Kepler-Poinsot
705:
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647:
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628:
625:
607:
579:
576:
575:
562:
558:
545:Maeder, Roman.
544:
543:
539:
534:
516:
440:dual polyhedron
434:
418:
401:
374:Star polyhedron
351:
334:
323:
310:
299:
266:
236:
207:
190:
172:Dual polyhedron
167:
160:
153:
137:
109:
104:
99:
94:
92:
88:Coxeter diagram
70:
28:
23:
22:
15:
12:
11:
5:
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624:
623:External links
621:
620:
619:
605:
574:
573:
565:Wenninger 2003
556:
536:
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529:
528:
522:
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512:
448:
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421:
420:
416:
413:
411:Symmetry group
407:
406:
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371:
367:
366:
358:
357:
350:
347:
344:
343:
327:
315:
314:
303:
265:
262:
258:hemipolyhedron
234:
233:, indexed as U
203:
202:
199:
197:Bowers acronym
193:
192:
183:
179:
178:
173:
169:
168:
165:
158:
151:
146:
140:
139:
135:
132:
130:Symmetry group
126:
125:
122:
120:Wythoff symbol
116:
115:
90:
84:
83:
80:
79:Faces by sides
76:
75:
60:
54:
53:
48:
44:
43:
35:
34:
26:
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14:
13:
10:
9:
6:
4:
3:
2:
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1024:
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1011:
1008:
1004:
999:
988:
985:
983:
980:
978:
975:
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945:
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928:
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923:
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918:
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908:
905:
903:
900:
898:
895:
893:
890:
888:
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878:
875:
874:
872:
866:
860:
857:
855:
852:
850:
847:
845:
842:
840:
837:
835:
832:
830:
827:
825:
822:
820:
817:
816:
814:
812:
811:hemipolyhedra
806:
800:
797:
795:
792:
790:
787:
785:
782:
780:
777:
775:
772:
770:
767:
765:
762:
760:
757:
756:
754:
746:
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737:
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732:
730:
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721:
719:
714:
708:
704:
697:
692:
690:
685:
683:
678:
677:
674:
668:
665:
660:
659:
654:
651:
646:
641:
640:
635:
632:
627:
626:
622:
616:
612:
608:
602:
598:
594:
590:
586:
582:
578:
577:
570:
566:
560:
557:
552:
548:
541:
538:
531:
526:
523:
521:
518:
517:
513:
511:
510:at infinity.
509:
504:
502:
498:
494:
490:
486:
482:
478:
474:
470:
465:
463:
459:
455:
446:
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441:
438:
437:
431:
428:
426:
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409:
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382:
379:
378:
375:
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369:
368:
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341:
337:
332:
326:
321:
316:
313:
308:
302:
297:
292:
289:
287:
283:
279:
275:
271:
263:
261:
259:
254:
252:
248:
247:vertex figure
244:
240:
232:
228:
224:
220:
210:
200:
198:
195:
194:
188:
184:
182:Vertex figure
181:
180:
177:
174:
171:
170:
164:
157:
150:
147:
145:
142:
141:
133:
131:
128:
127:
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121:
118:
117:
91:
89:
86:
85:
81:
78:
77:
73:
68:
64:
61:
59:
56:
55:
52:
49:
46:
45:
41:
36:
31:
19:
1023:expanding it
1012:
997:
853:
656:
637:
584:
559:
550:
540:
505:
500:
488:
473:dual figures
466:
453:
451:
444:
402:
397:
393:
324:
267:
255:
226:
222:
216:
82:12{5}+10{6}
71:
66:
62:
715:(nonconvex
585:Dual Models
551:MathConsult
489:Dual Models
340:convex hull
270:convex hull
1062:Categories
1015:polyhedron
532:References
497:stellation
191:5.6.5/4.6
752:polyhedra
713:polyhedra
658:MathWorld
639:MathWorld
583:(2003) ,
419:, , *532
280:with the
239:pentagons
138:, , *532
514:See also
508:vertices
477:vertices
389:Elements
383:—
256:It is a
243:hexagons
219:geometry
58:Elements
615:0730208
272:is the
241:and 10
229:) is a
201:Gidhei
613:
603:
569:p. 101
493:prisms
396:= 30,
221:, the
65:= 22,
1013:This
469:faces
249:is a
1019:stub
601:ISBN
452:The
400:= 60
380:Face
370:Type
268:Its
225:(or
69:= 60
47:Type
593:doi
487:'s
217:In
166:102
1064::
655:.
636:.
611:MR
609:,
599:,
591:,
587:,
567:,
549:.
464:.
433:65
430:DU
342:)
253:.
235:65
161:,
159:81
154:,
152:65
1050:e
1043:t
1036:v
1025:.
695:e
688:t
681:v
661:.
642:.
595::
571:)
563:(
553:.
417:h
415:I
403:V
398:E
394:F
338:(
163:W
156:C
149:U
136:h
134:I
72:V
67:E
63:F
20:)
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