171:
1330:
193:
1239:
1321:
1274:
1250:
29:
1261:
1296:
1285:
1414:
613:
371:
427:
1157:
1111:
751:
840:
1212:, (although the latter has 60 edges not contained in the great snub dodecicosidodecahedron). It shares its other 60 triangular faces (and its pentagrammic faces again) with the
1197:
948:
989:
1057:
1033:
674:
908:
789:
705:
867:
395:
1077:
636:
419:
285:
293:
1455:
608:{\displaystyle M={\begin{pmatrix}1/2&-\phi /2&1/(2\phi )\\\phi /2&1/(2\phi )&-1/2\\1/(2\phi )&1/2&\phi /2\end{pmatrix}}}
1300:
1228:
146:
1278:
1213:
246:
241:
117:
94:
89:
236:
84:
251:
99:
159:
1265:
1209:
139:
1448:
1289:
1220:
214:
1479:
1474:
1346:
1208:
It shares its vertices and edges, as well as 20 of its triangular faces and all its pentagrammic faces, with the
1122:
127:
170:
1441:
1082:
792:
39:
710:
798:
1329:
1238:
1320:
1273:
1249:
1169:
192:
28:
1393:
912:
46:
953:
180:
992:
870:
1260:
1038:
998:
641:
132:
876:
1390:
1295:
1425:
756:
679:
845:
380:
230:
76:
1062:
621:
404:
270:
107:
366:{\displaystyle p={\begin{pmatrix}\phi ^{-{\frac {1}{2}}}\\0\\\phi ^{-1}\end{pmatrix}}}
1468:
1367:
1116:
For a great snub dodecicosidodecahedron whose edge length is 1, the circumradius is
398:
1284:
1243:
1035:
are the vertices of a great snub dodecicosidodecahedron. The edge length equals
256:
1421:
1224:
1398:
226:
222:
202:
1413:
255:. It has the unusual feature that its 24 pentagram faces occur in 12
1231:, and the other 60 triangular faces occur in the other enantiomer.
190:
842:
with an even number of minus signs. The transformations
1429:
1223:. In addition, 20 of the triangular faces occur in one
442:
308:
1172:
1125:
1085:
1065:
1041:
1001:
956:
915:
879:
848:
801:
759:
713:
682:
644:
624:
430:
407:
383:
296:
273:
1315:
1233:
18:
991:constitute the group of rotational symmetries of a
869:constitute the group of rotational symmetries of a
707:, counterclockwise. Let the linear transformations
1191:
1151:
1105:
1071:
1051:
1027:
983:
942:
902:
861:
834:
783:
745:
699:
668:
630:
607:
413:
389:
365:
279:
1219:The edges and triangular faces also occur in the
197:3D model of a great snub dodecicosidodecahedron
1449:
8:
1152:{\displaystyle R={\frac {1}{2}}{\sqrt {2}}}
1456:
1442:
753:be the transformations which send a point
1179:
1171:
1142:
1132:
1124:
1106:{\displaystyle {\frac {1}{2}}{\sqrt {2}}}
1096:
1086:
1084:
1064:
1042:
1040:
1016:
1006:
1000:
955:
914:
894:
884:
878:
853:
847:
800:
758:
737:
718:
712:
689:
681:
643:
623:
589:
576:
554:
539:
514:
501:
477:
464:
448:
437:
429:
406:
382:
346:
319:
315:
303:
295:
272:
1368:"64: great snub dodecicosidodecahedron"
1358:
229:), 180 edges, and 60 vertices. It has
1301:Compound of twenty tetrahemihexahedra
1229:compound of twenty tetrahemihexahedra
7:
1410:
1408:
746:{\displaystyle T_{0},\ldots ,T_{11}}
1394:"Great snub dodecicosidodecahedron"
835:{\displaystyle (\pm x,\pm y,\pm z)}
1428:. You can help Knowledge (XXG) by
22:Great snub dodecicosidodecahedron
14:
1279:Great disnub dirhombidodecahedron
1255:Great snub dodecicosidodecahedron
1214:great disnub dirhombidodecahedron
211:great snub dodekicosidodecahedron
207:great snub dodecicosidodecahedron
1412:
1328:
1319:
1294:
1283:
1272:
1259:
1248:
1237:
1192:{\displaystyle r={\frac {1}{2}}}
638:is the rotation around the axis
249:
244:
239:
234:
169:
97:
92:
87:
82:
27:
943:{\displaystyle (i=0,\ldots ,11}
160:Great hexagonal hexecontahedron
1266:Great dirhombicosidodecahedron
1210:great dirhombicosidodecahedron
984:{\displaystyle j=0,\ldots ,4)}
978:
916:
829:
802:
778:
760:
663:
645:
568:
559:
528:
519:
491:
482:
1:
1327:
1318:
1290:Compound of twenty octahedra
1221:compound of twenty octahedra
215:nonconvex uniform polyhedron
1079:, and the midradius equals
1052:{\displaystyle {\sqrt {2}}}
1028:{\displaystyle T_{i}M^{j}p}
669:{\displaystyle (1,0,\phi )}
1496:
1407:
1059:, the circumradius equals
903:{\displaystyle T_{i}M^{j}}
1347:List of uniform polyhedra
26:
21:
16:Polyhedron with 104 faces
71:(20+60){3}+(12+12){5/2}
784:{\displaystyle (x,y,z)}
700:{\displaystyle 2\pi /5}
221:. It has 104 faces (80
40:Uniform star polyhedron
1424:-related article is a
1193:
1153:
1107:
1073:
1053:
1029:
985:
944:
904:
873:. The transformations
863:
836:
785:
747:
701:
670:
632:
609:
415:
391:
367:
281:
198:
1194:
1154:
1108:
1074:
1054:
1030:
995:. Then the 60 points
986:
945:
905:
864:
862:{\displaystyle T_{i}}
837:
786:
748:
702:
671:
633:
610:
416:
392:
390:{\displaystyle \phi }
368:
282:
263:Cartesian coordinates
196:
63:= 60 (χ = −16)
1325:Traditional filling
1170:
1123:
1083:
1063:
1039:
999:
954:
913:
877:
846:
799:
757:
711:
680:
642:
622:
428:
405:
381:
294:
271:
993:regular icosahedron
871:regular tetrahedron
1391:Weisstein, Eric W.
1189:
1149:
1103:
1069:
1049:
1025:
981:
940:
900:
859:
832:
781:
743:
697:
666:
628:
605:
599:
411:
387:
363:
357:
277:
199:
1480:Uniform polyhedra
1437:
1436:
1338:
1337:
1334:Modulo-2 filling
1306:
1305:
1204:Related polyhedra
1187:
1163:Its midradius is
1147:
1140:
1101:
1094:
1072:{\displaystyle 1}
1047:
793:even permutations
631:{\displaystyle M}
414:{\displaystyle M}
401:. Let the matrix
327:
280:{\displaystyle p}
189:
188:
112:| 5/3 5/2 3
1487:
1475:Polyhedron stubs
1458:
1451:
1444:
1416:
1409:
1404:
1403:
1376:
1375:
1363:
1332:
1323:
1316:
1298:
1287:
1276:
1263:
1252:
1241:
1234:
1198:
1196:
1195:
1190:
1188:
1180:
1158:
1156:
1155:
1150:
1148:
1143:
1141:
1133:
1112:
1110:
1109:
1104:
1102:
1097:
1095:
1087:
1078:
1076:
1075:
1070:
1058:
1056:
1055:
1050:
1048:
1043:
1034:
1032:
1031:
1026:
1021:
1020:
1011:
1010:
990:
988:
987:
982:
949:
947:
946:
941:
909:
907:
906:
901:
899:
898:
889:
888:
868:
866:
865:
860:
858:
857:
841:
839:
838:
833:
790:
788:
787:
782:
752:
750:
749:
744:
742:
741:
723:
722:
706:
704:
703:
698:
693:
675:
673:
672:
667:
637:
635:
634:
629:
614:
612:
611:
606:
604:
603:
593:
580:
558:
543:
518:
505:
481:
468:
452:
420:
418:
417:
412:
396:
394:
393:
388:
372:
370:
369:
364:
362:
361:
354:
353:
330:
329:
328:
320:
286:
284:
283:
278:
254:
253:
252:
248:
247:
243:
242:
238:
237:
195:
175:3.3.3.5/2.3.5/3
173:
128:Index references
102:
101:
100:
96:
95:
91:
90:
86:
85:
31:
19:
1495:
1494:
1490:
1489:
1488:
1486:
1485:
1484:
1465:
1464:
1463:
1462:
1389:
1388:
1385:
1380:
1379:
1366:Maeder, Roman.
1365:
1364:
1360:
1355:
1343:
1333:
1324:
1313:
1311:
1299:
1288:
1277:
1264:
1253:
1242:
1206:
1168:
1167:
1121:
1120:
1081:
1080:
1061:
1060:
1037:
1036:
1012:
1002:
997:
996:
952:
951:
911:
910:
890:
880:
875:
874:
849:
844:
843:
797:
796:
755:
754:
733:
714:
709:
708:
678:
677:
676:by an angle of
640:
639:
620:
619:
598:
597:
584:
571:
548:
547:
531:
509:
495:
494:
472:
456:
438:
426:
425:
403:
402:
379:
378:
356:
355:
342:
339:
338:
332:
331:
311:
304:
292:
291:
269:
268:
265:
250:
245:
240:
235:
233:
231:Coxeter diagram
220:
191:
174:
156:Dual polyhedron
151:
144:
137:
98:
93:
88:
83:
81:
77:Coxeter diagram
59:
17:
12:
11:
5:
1493:
1491:
1483:
1482:
1477:
1467:
1466:
1461:
1460:
1453:
1446:
1438:
1435:
1434:
1417:
1406:
1405:
1384:
1383:External links
1381:
1378:
1377:
1357:
1356:
1354:
1351:
1350:
1349:
1342:
1339:
1336:
1335:
1326:
1310:
1307:
1304:
1303:
1292:
1281:
1269:
1268:
1257:
1246:
1205:
1202:
1201:
1200:
1186:
1183:
1178:
1175:
1161:
1160:
1146:
1139:
1136:
1131:
1128:
1100:
1093:
1090:
1068:
1046:
1024:
1019:
1015:
1009:
1005:
980:
977:
974:
971:
968:
965:
962:
959:
939:
936:
933:
930:
927:
924:
921:
918:
897:
893:
887:
883:
856:
852:
831:
828:
825:
822:
819:
816:
813:
810:
807:
804:
780:
777:
774:
771:
768:
765:
762:
740:
736:
732:
729:
726:
721:
717:
696:
692:
688:
685:
665:
662:
659:
656:
653:
650:
647:
627:
617:
616:
602:
596:
592:
588:
585:
583:
579:
575:
572:
570:
567:
564:
561:
557:
553:
550:
549:
546:
542:
538:
535:
532:
530:
527:
524:
521:
517:
513:
510:
508:
504:
500:
497:
496:
493:
490:
487:
484:
480:
476:
473:
471:
467:
463:
460:
457:
455:
451:
447:
444:
443:
441:
436:
433:
410:
386:
375:
374:
360:
352:
349:
345:
341:
340:
337:
334:
333:
326:
323:
318:
314:
310:
309:
307:
302:
299:
276:
267:Let the point
264:
261:
218:
217:, indexed as U
187:
186:
183:
181:Bowers acronym
177:
176:
167:
163:
162:
157:
153:
152:
149:
142:
135:
130:
124:
123:
120:
118:Symmetry group
114:
113:
110:
108:Wythoff symbol
104:
103:
79:
73:
72:
69:
68:Faces by sides
65:
64:
49:
43:
42:
37:
33:
32:
24:
23:
15:
13:
10:
9:
6:
4:
3:
2:
1492:
1481:
1478:
1476:
1473:
1472:
1470:
1459:
1454:
1452:
1447:
1445:
1440:
1439:
1433:
1431:
1427:
1423:
1418:
1415:
1411:
1401:
1400:
1395:
1392:
1387:
1386:
1382:
1373:
1369:
1362:
1359:
1352:
1348:
1345:
1344:
1340:
1331:
1322:
1317:
1314:
1308:
1302:
1297:
1293:
1291:
1286:
1282:
1280:
1275:
1271:
1270:
1267:
1262:
1258:
1256:
1251:
1247:
1245:
1240:
1236:
1235:
1232:
1230:
1226:
1222:
1217:
1215:
1211:
1203:
1184:
1181:
1176:
1173:
1166:
1165:
1164:
1144:
1137:
1134:
1129:
1126:
1119:
1118:
1117:
1114:
1098:
1091:
1088:
1066:
1044:
1022:
1017:
1013:
1007:
1003:
994:
975:
972:
969:
966:
963:
960:
957:
937:
934:
931:
928:
925:
922:
919:
895:
891:
885:
881:
872:
854:
850:
826:
823:
820:
817:
814:
811:
808:
805:
794:
775:
772:
769:
766:
763:
738:
734:
730:
727:
724:
719:
715:
694:
690:
686:
683:
660:
657:
654:
651:
648:
625:
600:
594:
590:
586:
581:
577:
573:
565:
562:
555:
551:
544:
540:
536:
533:
525:
522:
515:
511:
506:
502:
498:
488:
485:
478:
474:
469:
465:
461:
458:
453:
449:
445:
439:
434:
431:
424:
423:
422:
408:
400:
384:
358:
350:
347:
343:
335:
324:
321:
316:
312:
305:
300:
297:
290:
289:
288:
274:
262:
260:
258:
232:
228:
224:
216:
212:
208:
204:
194:
184:
182:
179:
178:
172:
168:
166:Vertex figure
165:
164:
161:
158:
155:
154:
148:
141:
134:
131:
129:
126:
125:
121:
119:
116:
115:
111:
109:
106:
105:
80:
78:
75:
74:
70:
67:
66:
62:
57:
53:
50:
48:
45:
44:
41:
38:
35:
34:
30:
25:
20:
1430:expanding it
1419:
1397:
1371:
1361:
1312:
1254:
1218:
1207:
1162:
1115:
618:
421:be given by
399:golden ratio
376:
287:be given by
266:
210:
206:
200:
60:
55:
51:
1372:MathConsult
1244:Convex hull
1469:Categories
1422:polyhedron
1353:References
1225:enantiomer
227:pentagrams
1399:MathWorld
970:…
932:…
824:±
815:±
806:±
728:…
687:π
661:ϕ
587:ϕ
566:ϕ
534:−
526:ϕ
499:ϕ
489:ϕ
462:ϕ
459:−
385:ϕ
348:−
344:ϕ
317:−
313:ϕ
223:triangles
122:I, , 532
1341:See also
257:coplanar
203:geometry
47:Elements
1309:Gallery
1227:of the
791:to the
397:is the
259:pairs.
225:and 24
213:) is a
185:Gisdid
54:= 104,
377:where
205:, the
1420:This
58:= 180
1426:stub
209:(or
36:Type
795:of
201:In
150:115
1471::
1396:.
1370:.
1216:.
1113:.
950:,
938:11
739:11
219:64
145:,
143:80
138:,
136:64
1457:e
1450:t
1443:v
1432:.
1402:.
1374:.
1199:.
1185:2
1182:1
1177:=
1174:r
1159:.
1145:2
1138:2
1135:1
1130:=
1127:R
1099:2
1092:2
1089:1
1067:1
1045:2
1023:p
1018:j
1014:M
1008:i
1004:T
979:)
976:4
973:,
967:,
964:0
961:=
958:j
935:,
929:,
926:0
923:=
920:i
917:(
896:j
892:M
886:i
882:T
855:i
851:T
830:)
827:z
821:,
818:y
812:,
809:x
803:(
779:)
776:z
773:,
770:y
767:,
764:x
761:(
735:T
731:,
725:,
720:0
716:T
695:5
691:/
684:2
664:)
658:,
655:0
652:,
649:1
646:(
626:M
615:.
601:)
595:2
591:/
582:2
578:/
574:1
569:)
563:2
560:(
556:/
552:1
545:2
541:/
537:1
529:)
523:2
520:(
516:/
512:1
507:2
503:/
492:)
486:2
483:(
479:/
475:1
470:2
466:/
454:2
450:/
446:1
440:(
435:=
432:M
409:M
373:,
359:)
351:1
336:0
325:2
322:1
306:(
301:=
298:p
275:p
147:W
140:C
133:U
61:V
56:E
52:F
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