206:
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178:
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171:
517:
393:
389:
364:
350:
357:
382:
378:
606:
152:
142:
500:
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129:
having a symmetry of order 3 (triangular symmetry) acting with 2 rotational orbits on the 6 angles of the vertex figure (the word
482:
410:
405:
904:
147:
492:
794:
468:
205:
191:
488:
788:
916:
844:
764:
599:
32:
363:
349:
198:
850:
524:
Philosophical
Transactions of the Royal Society of London. Series A. Mathematical and Physical Sciences
177:
163:
531:
213:
90:
356:
987:
961:
838:
832:
592:
571:
555:
170:
951:
875:
827:
800:
770:
547:
956:
936:
758:
539:
567:
910:
822:
817:
782:
737:
727:
717:
712:
563:
343:
535:
966:
869:
732:
722:
327:
36:
448:
981:
887:
881:
776:
707:
697:
575:
185:
702:
742:
676:
666:
656:
651:
927:
681:
671:
661:
646:
636:
615:
551:
941:
86:
28:
There are five uniform ditrigonal polyhedra, all with icosahedral symmetry.
543:
20:, there are seven uniform and uniform dual polyhedra named as ditrigonal.
641:
82:
78:
17:
946:
464:
126:
559:
77:
are not 2. Each polyhedron includes two types of faces, being of
125:) with a symmetry of order 3. Here, term ditrigonal refers to a
588:
522:
Skilling, J. (1975), "The complete set of uniform polyhedra",
584:
135:
926:
897:
862:
810:
751:
690:
629:
516:, Ph.D. Dissertation, University of Toronto, 1966
514:The Theory of Uniform Polytopes and Honeycombs
600:
394:great ditrigonal dodecacronic hexecontahedron
390:small ditrigonal dodecacronic hexecontahedron
8:
607:
593:
585:
487:, Geometriae Dedicata 47, 57–110, 1993.
435:
433:
431:
484:Uniform Solution for Uniform Polyhedra.
427:
383:great ditrigonal dodecicosidodecahedron
379:small ditrigonal dodecicosidodecahedron
133:means "having two sets of 3 angles").
471:and J.C.P Miller, Uniform Polyhedra,
7:
451:, Mathworld (retrieved 10 June 2016)
624:Listed by number of faces and type
373:Other uniform ditrigonal polyhedra
153:Great ditrigonal icosidodecahedron
143:Small ditrigonal icosidodecahedron
14:
388:Their duals are respectively the
362:
355:
348:
204:
197:
190:
176:
169:
162:
411:Great complex icosidodecahedron
406:Small complex icosidodecahedron
1:
835:(two infinite groups and 75)
148:Ditrigonal dodecadodecahedron
853:(two infinite groups and 50)
341:
325:
285:
211:
183:
157:
69:are ditrigonal, at least if
1004:
905:Kepler–Poinsot polyhedron
622:
24:Ditrigonal vertex figures
478:(1954) pp. 401–450.
917:Uniform star polyhedron
845:quasiregular polyhedron
33:uniform star polyhedron
851:semiregular polyhedron
544:10.1098/rsta.1975.0022
898:non-convex polyhedron
91:vertex configurations
469:M.S. Longuet-Higgins
214:Vertex configuration
536:1975RSPTA.278..111S
839:regular polyhedron
833:uniform polyhedron
795:Hectotriadiohedron
449:Uniform Polyhedron
385:are also uniform.
975:
974:
876:Archimedean solid
863:convex polyhedron
771:Icosidodecahedron
530:(1278): 111–135,
370:
369:
995:
811:elemental things
789:Enneacontahedron
759:Icositetrahedron
609:
602:
595:
586:
578:
493:Kaleido software
452:
446:
440:
437:
366:
359:
352:
316:
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296:
282:(3.5.3.5.3.5)/2
279:
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136:
93:are of the form
61:
59:
58:
55:
52:
39:of the form 3 |
1003:
1002:
998:
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994:
993:
992:
978:
977:
976:
971:
922:
911:Star polyhedron
893:
858:
806:
783:Hexecontahedron
765:Triacontahedron
747:
738:Enneadecahedron
728:Heptadecahedron
718:Pentadecahedron
713:Tetradecahedron
686:
625:
618:
613:
582:
521:
509:
507:Further reading
465:Coxeter, H.S.M.
461:
456:
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447:
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438:
429:
424:
419:
402:
375:
344:Coxeter diagram
338:3 | 3/2 5
335:3 | 5/3 5
332:3 | 5/2 3
322:20 {3}, 12 {5}
321:
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56:
53:
50:
49:
47:
26:
12:
11:
5:
1001:
999:
991:
990:
980:
979:
973:
972:
970:
969:
967:parallelepiped
964:
959:
954:
949:
944:
939:
933:
931:
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923:
921:
920:
914:
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901:
899:
895:
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870:Platonic solid
866:
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859:
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856:
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854:
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808:
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804:
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792:
786:
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768:
762:
755:
753:
749:
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745:
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735:
733:Octadecahedron
730:
725:
723:Hexadecahedron
720:
715:
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685:
684:
679:
674:
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633:
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604:
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503:
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398:
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353:
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328:Wythoff symbol
324:
323:
318:
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288:
284:
283:
280:
248:
216:
210:
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195:
188:
182:
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174:
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37:Wythoff symbol
25:
22:
13:
10:
9:
6:
4:
3:
2:
1000:
989:
986:
985:
983:
968:
965:
963:
960:
958:
955:
953:
950:
948:
945:
943:
940:
938:
935:
934:
932:
929:
925:
918:
915:
912:
909:
906:
903:
902:
900:
896:
889:
888:Johnson solid
886:
883:
882:Catalan solid
880:
877:
874:
871:
868:
867:
865:
861:
852:
849:
846:
843:
840:
837:
836:
834:
831:
829:
826:
824:
821:
819:
816:
815:
813:
809:
802:
799:
796:
793:
790:
787:
784:
781:
778:
777:Hexoctahedron
775:
772:
769:
766:
763:
760:
757:
756:
754:
750:
744:
741:
739:
736:
734:
731:
729:
726:
724:
721:
719:
716:
714:
711:
709:
708:Tridecahedron
706:
704:
701:
699:
698:Hendecahedron
696:
695:
693:
689:
683:
680:
678:
675:
673:
670:
668:
665:
663:
660:
658:
655:
653:
650:
648:
645:
643:
640:
638:
635:
634:
632:
628:
621:
617:
610:
605:
603:
598:
596:
591:
590:
587:
583:
577:
573:
569:
565:
561:
557:
553:
549:
545:
541:
537:
533:
529:
525:
520:
518:
515:
512:Johnson, N.;
511:
510:
506:
502:
498:
494:
490:
486:
485:
480:
477:
474:
470:
466:
463:
462:
458:
450:
445:
442:
436:
434:
432:
428:
421:
416:
412:
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407:
404:
403:
399:
397:
395:
391:
386:
384:
380:
372:
365:
361:
358:
354:
351:
347:
345:
342:
337:
334:
331:
329:
326:
319:
307:12 {5}, 12 {
304:
292:20 {3}, 12 {
289:
286:
281:
249:
217:
215:
212:
207:
203:
200:
196:
193:
189:
187:
186:Vertex figure
184:
179:
175:
172:
168:
165:
161:
158:
154:
151:
149:
146:
144:
141:
138:
137:
134:
132:
128:
124:
120:
116:
112:
108:
104:
100:
96:
92:
88:
84:
80:
76:
72:
68:
65:
45:
42:
38:
34:
29:
23:
21:
19:
801:Apeirohedron
752:>20 faces
703:Dodecahedron
581:
527:
523:
513:
483:
475:
473:Phil. Trans.
472:
459:Bibliography
444:
439:Har'El, 1993
387:
376:
130:
122:
118:
114:
110:
106:
102:
98:
94:
74:
70:
66:
63:
43:
40:
30:
27:
15:
743:Icosahedron
691:11–20 faces
677:Enneahedron
667:Heptahedron
657:Pentahedron
652:Tetrahedron
501:dual images
481:Har'El, Z.
928:prismatoid
913:(infinite)
682:Decahedron
672:Octahedron
662:Hexahedron
637:Monohedron
630:1–10 faces
489:Zvi Har’El
417:References
131:ditrigonal
87:pentagrams
31:The three
988:Polyhedra
942:antiprism
647:Trihedron
616:Polyhedra
576:122634260
552:0080-4614
83:pentagons
79:triangles
982:Category
642:Dihedron
400:See also
381:and the
89:. Their
18:geometry
962:pyramid
947:frustum
568:0365333
532:Bibcode
312:⁄
297:⁄
275:⁄
265:⁄
255:⁄
243:⁄
233:⁄
223:⁄
127:hexagon
60:
48:
952:cupola
828:vertex
574:
566:
558:
550:
497:Images
287:Faces
159:Image
957:wedge
937:prism
797:(132)
572:S2CID
560:74475
556:JSTOR
476:246 A
422:Notes
139:Type
85:, or
35:with
919:(57)
890:(92)
884:(13)
878:(13)
847:(16)
823:edge
818:face
791:(90)
785:(60)
779:(48)
773:(32)
767:(30)
761:(24)
548:ISSN
392:and
377:The
117:or (
73:and
907:(4)
872:(5)
841:(9)
803:(∞)
540:doi
528:278
270:.5.
260:.5.
238:.3.
228:.3.
46:or
16:In
984::
930:s
570:,
564:MR
562:,
554:,
546:,
538:,
526:,
499:,
495:,
491:,
467:,
430:^
396:.
320:32
317:}
305:24
302:}
290:32
250:5.
218:3.
81:,
62:|
608:e
601:t
594:v
542::
534::
314:2
310:5
299:2
295:5
277:3
273:5
267:3
263:5
257:3
253:5
245:2
241:5
235:2
231:5
225:2
221:5
123:q
121:.
119:p
115:q
113:.
111:p
109:.
107:q
105:.
103:p
101:.
99:q
97:.
95:p
75:q
71:p
67:q
64:p
57:2
54:/
51:3
44:q
41:p
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