13484:
15567:
13549:
14499:
17358:
13204:
11050:
15474:
13211:
12701:
13489:
16227:
13049:
12519:
10506:
14768:
13260:
9138:
15526:
14080:
10988:
8240:
13678:
17095:
16496:
16249:
14779:
13271:
8233:
15537:
14091:
9679:
9672:
9658:
9651:
9171:
9665:
13913:
10520:
15714:
10513:
16525:
12159:
16876:
4300:
9182:
4101:
4094:
4087:
3567:
3560:
3553:
2624:
2617:
2610:
14254:
13935:
13042:
12514:
4219:
15921:
9639:
9632:
9618:
9611:
9625:
14924:
1447:
1386:
14584:
14577:
14570:
12784:
12777:
12770:
12953:
10492:
9343:
15176:
15169:
15162:
14558:
14551:
14544:
12758:
12751:
12744:
12296:
12946:
11712:
11626:
10499:
8247:
17146:
15150:
15143:
15136:
14721:
13723:
8405:
15465:
14343:
15339:
15332:
11904:
11897:
11890:
10593:
10565:
9145:
8613:
8226:
7447:
3707:
11878:
11871:
11864:
10572:
2582:
10586:
10579:
13174:
12138:
8855:
8848:
8841:
7692:
7685:
7678:
6425:
4059:
3525:
12605:
14478:
12678:
12131:
11806:
8829:
8822:
8815:
7666:
7659:
7652:
4241:
3803:
15425:
10430:
10424:
10415:
10409:
10400:
9004:
6783:
6100:
16181:
15668:
13874:
13445:
13436:
10965:
7958:
7951:
7944:
15418:
1316:
1164:
14880:
12461:
10478:
10472:
10463:
10457:
10451:
10445:
10436:
9011:
6576:
8376:
15719:
9439:
7937:
16457:
16172:
14201:
14192:
13865:
12470:
11596:
9300:
8574:
11785:
9207:
12152:
15018:
17330:
15686:
13454:
11605:
10956:
8583:
7417:
7408:
149:
34:
1547:
1098:
1007:
7533:
174:
4230:
4208:
4146:
3746:
3650:
2753:
15998:
14611:
14616:
15481:
1636:
1629:
1643:
8700:
1610:
1603:
15087:
1617:
4157:
2792:
4080:
2603:
16068:
16054:
16031:
16061:
16047:
16038:
16825:
262:
4073:
3546:
3539:
2596:
8768:
7605:
17321:
17052:
17043:
16783:
16466:
16199:
16190:
15677:
14219:
13883:
12479:
11614:
6193:
14485:
29:
4263:
4252:
3904:
3842:
4066:
3532:
2589:
16774:
14889:
14210:
16015:
563:
577:
4179:
4168:
2870:
2831:
4197:
3611:
556:
4135:
570:
2714:
12684:
11790:
4113:
2636:
16024:
11813:
4124:
2675:
15093:
8773:
7610:
584:
9213:
15456:
14492:
11077:
is non-uniform, with the highest symmetry construction reflecting an alternation of the uniform bitruncated cubic honeycomb. A lower-symmetry construction involves regular icosahedra paired with golden icosahedra (with 8 equilateral triangles paired with 12 golden triangles). There are three
9463:
15446:. The first has octagons removed, and vertex configuration 4.4.4.6. It can be seen as truncated cuboctahedra and octagonal prisms augmented together. The second can be seen as augmented octagonal prisms, vertex configuration 4.8.4.8.
13669:
Despite being non-uniform, there is a near-miss version with two edge lengths shown below, one of which is around 4.3% greater than the other. The snub cubes in this case are uniform, but the rest of the cells are not.
13168:
A cell can be as 1/24 of a translational cube with vertices positioned: taking two corner, ne face center, and the cube center. The edge colors and labels specify how many cells exist around the edge.
15494:
Nonuniform variants with symmetry and two types of truncated cuboctahedra can be doubled by placing the two types of truncated cuboctahedra on each other to produce a nonuniform honeycomb with
13193:
4.4.6.6, with the octagons and some of the squares removed. It can be seen as constructed by augmenting truncated cuboctahedral cells, or by augmenting alternated truncated octahedra and cubes.
17088:
15201:. The symmetry can be doubled by relating the first and last branches of the Coxeter diagram, which can be shown with one color for all the truncated cuboctahedral and octagonal prism cells.
16818:
18010:
17895:
17852:
17809:
17766:
6386:
6352:
10171:
10103:
10065:
10017:
10007:
6255:
6216:
17968:
17932:
15286:
15248:
15002:
14710:
14307:
13163:
12901:
12861:
12569:
12024:
11984:
11696:
11034:
10220:
10152:
10056:
9960:
9862:
9738:
9420:
8970:
8932:
8683:
7883:
7844:
7805:
7766:
7516:
7023:
6985:
6903:
6865:
6728:
6687:
6526:
6335:
6294:
6169:
6024:
5542:
5509:
5476:
5443:
5372:
5132:
5091:
4793:
3958:
3512:
3159:
3144:
3129:
2559:
2516:
1960:
1945:
1930:
1917:
1902:
1887:
1493:
1478:
1463:
1431:
1416:
1401:
1300:
1285:
1270:
953:
938:
923:
243:
15393:
11376:
11366:
11279:
10606:
Nonuniform variants with symmetry and two types of truncated octahedra can be doubled by placing the two types of truncated octahedra to produce a nonuniform honeycomb with
10383:
10373:
10257:
10241:
10231:
9921:
9911:
7041:
7031:
6921:
6911:
6815:
6806:
6796:
6599:
6537:
6438:
5740:
5614:
5595:
5233:
5210:
5174:
5164:
5100:
3164:
3149:
3134:
2554:
2549:
2511:
2506:
2396:
2391:
2353:
2348:
2173:
2135:
1965:
1950:
1935:
1922:
1907:
1892:
1498:
1483:
1468:
1436:
1421:
1406:
1305:
1290:
1275:
958:
943:
928:
15403:
13624:
13382:
13027:
12407:
12118:
11542:
11395:
11357:
11162:
11144:
10892:
10816:
10770:
10354:
10315:
8162:
7354:
7232:
6745:
5971:
5938:
5905:
5872:
5689:
5243:
5197:
5047:
5025:
3316:
2569:
2411:
2183:
1196:
15908:
15898:
15888:
15878:
14672:
14652:
14642:
13750:
13740:
13730:
13531:
13521:
13511:
13420:
13115:
13105:
13095:
12445:
12273:
12253:
11580:
10940:
10910:
10844:
10808:
10181:
10161:
10113:
10093:
10075:
9989:
9979:
9893:
9883:
9084:
8558:
8122:
8092:
8053:
8044:
7392:
7362:
7334:
7306:
7270:
7204:
6638:
6628:
6609:
6589:
6487:
6457:
6245:
6226:
6206:
5730:
5720:
5669:
5636:
5575:
5411:
5391:
5381:
5362:
5352:
4954:
4911:
4868:
4825:
4813:
4803:
4784:
4774:
4754:
4464:
4454:
4444:
4434:
1087:
17432:
17422:
17412:
17295:
17285:
17275:
17265:
17247:
17237:
17227:
17017:
17007:
16997:
16987:
16969:
16949:
16939:
16748:
16738:
16728:
16718:
16700:
16680:
16670:
16585:
16575:
16565:
16555:
16437:
16427:
16417:
16407:
16313:
16303:
16293:
16283:
16152:
16142:
16132:
16122:
15808:
15798:
15788:
15778:
15652:
15642:
15632:
15622:
15384:
15374:
15364:
15354:
14864:
14854:
14844:
14834:
14444:
14424:
14414:
14176:
14156:
14146:
13997:
13987:
13977:
13835:
13825:
13815:
13705:
13695:
13685:
13652:
13642:
13632:
13619:
13614:
13604:
13410:
13400:
13390:
13377:
13372:
13362:
13344:
13334:
13324:
13022:
13017:
13007:
12988:
12978:
12968:
12435:
12425:
12415:
12402:
12397:
12387:
12369:
12359:
12349:
12113:
12098:
12079:
12059:
11570:
11550:
11537:
11522:
11504:
11484:
11405:
11400:
11390:
11385:
11352:
11347:
11318:
11308:
11172:
11167:
11157:
11152:
11139:
11134:
11106:
11096:
10930:
10920:
10902:
10897:
10887:
10882:
10864:
10854:
10826:
10821:
10798:
10788:
10765:
10760:
10732:
10722:
10364:
10359:
10349:
10344:
10325:
10320:
10296:
10286:
10176:
10166:
10108:
10098:
10070:
9274:
9264:
9103:
9093:
9064:
9054:
9041:
9036:
9026:
8538:
8528:
8515:
8510:
8500:
8472:
8462:
8358:
8338:
8328:
8211:
8206:
8196:
8191:
8167:
8148:
8143:
8102:
8063:
8024:
7985:
7372:
7349:
7321:
7316:
7298:
7293:
7283:
7278:
7260:
7227:
7184:
7161:
7156:
7118:
6750:
6740:
6604:
6594:
6547:
6448:
6396:
6391:
6381:
6376:
6357:
6347:
6250:
6221:
6211:
6125:
6115:
5966:
5961:
5951:
5933:
5928:
5900:
5885:
5867:
5834:
5829:
5819:
5801:
5796:
5768:
5753:
5735:
5684:
5651:
5619:
5609:
5604:
5590:
5537:
5532:
5522:
5504:
5499:
5471:
5456:
5438:
5367:
5277:
5187:
5122:
5110:
5081:
5037:
5015:
4984:
4974:
4941:
4888:
4798:
4722:
4702:
4692:
4669:
4659:
4649:
4625:
4605:
4572:
4562:
4529:
4476:
3953:
3948:
3943:
3915:
3896:
3891:
3886:
3881:
3853:
3814:
3795:
3790:
3785:
3757:
3718:
3694:
3689:
3661:
3622:
3583:
3507:
3502:
3487:
3449:
3435:
3430:
3425:
3410:
3372:
3329:
3306:
3301:
3286:
3278:
3273:
3258:
3220:
3177:
3116:
3101:
3063:
3020:
2977:
2881:
2842:
2803:
2764:
2725:
2686:
2647:
2544:
2534:
2501:
2478:
2463:
2425:
2401:
2386:
2376:
2358:
2343:
2320:
2305:
2267:
2249:
2234:
2196:
2168:
2163:
2153:
2130:
2125:
2102:
2087:
2049:
2031:
2016:
1978:
1874:
1859:
1821:
1803:
1788:
1750:
1536:
1526:
1516:
1506:
1361:
1341:
1261:
1251:
1221:
1186:
1149:
1119:
1057:
1044:
1029:
986:
976:
966:
885:
791:
769:
739:
720:
700:
680:
103:
17437:
17300:
17252:
17022:
16974:
16753:
16705:
11289:
10267:
9046:
8520:
8201:
8153:
7326:
7288:
7166:
6825:
6120:
5839:
5806:
5773:
5656:
5282:
5220:
3930:
3699:
3474:
3291:
3121:
2886:
2539:
2526:
2496:
2483:
2468:
2430:
2381:
2368:
2338:
2325:
2254:
2158:
2145:
2120:
2107:
2036:
1879:
1808:
1366:
1256:
1049:
774:
725:
705:
685:
17523:
For cross-referencing, they are given with list indices from
Andreini (1-22), Williams(1-2,9-19), Johnson (11-19, 21-25, 31-34, 41-49, 51-52, 61-65), and Grünbaum(1-28).
17442:
17402:
17305:
17257:
17217:
17027:
16979:
16959:
16758:
16710:
16690:
15398:
14662:
14434:
14166:
14007:
13845:
13760:
13715:
13662:
13541:
13354:
13125:
12998:
12379:
12283:
12263:
12108:
12089:
12069:
11560:
11532:
11514:
11494:
11337:
11328:
11298:
11284:
11124:
11116:
11086:
10874:
10836:
10778:
10750:
10742:
10712:
10335:
10306:
10276:
10262:
10085:
9999:
9969:
9903:
9873:
9284:
9254:
9123:
9113:
9074:
8548:
8492:
8482:
8348:
8182:
8172:
8133:
8112:
8083:
8073:
8034:
8014:
8005:
7995:
7975:
7382:
7344:
7250:
7240:
7222:
7212:
7194:
7174:
7146:
7138:
7128:
7108:
6820:
6755:
6735:
6648:
6618:
6477:
6467:
6362:
6342:
6235:
6130:
6110:
5918:
5895:
5862:
5852:
5786:
5763:
5679:
5646:
5624:
5585:
5489:
5466:
5433:
5423:
5401:
5272:
5262:
5238:
5215:
5192:
5169:
5127:
5086:
5042:
5020:
4964:
4931:
4921:
4898:
4878:
4855:
4845:
4835:
4764:
4712:
4679:
4635:
4615:
4592:
4582:
4549:
4539:
4519:
4506:
4496:
4486:
4362:
4352:
4342:
4332:
3935:
3925:
3873:
3863:
3834:
3824:
3777:
3767:
3738:
3728:
3681:
3671:
3642:
3632:
3603:
3593:
3497:
3479:
3469:
3459:
3420:
3402:
3392:
3382:
3359:
3349:
3339:
3311:
3296:
3268:
3250:
3240:
3230:
3207:
3197:
3187:
3111:
3093:
3083:
3073:
3050:
3040:
3030:
3007:
2997:
2987:
2901:
2891:
2862:
2852:
2823:
2813:
2784:
2774:
2745:
2735:
2706:
2696:
2667:
2657:
2564:
2521:
2491:
2473:
2455:
2445:
2435:
2406:
2363:
2333:
2315:
2297:
2287:
2277:
2244:
2226:
2216:
2206:
2178:
2140:
2115:
2097:
2079:
2069:
2059:
2026:
2008:
1998:
1988:
1869:
1851:
1841:
1831:
1798:
1780:
1770:
1760:
1371:
1351:
1331:
1241:
1231:
1191:
1139:
1129:
1077:
1067:
1039:
996:
915:
905:
895:
821:
811:
801:
779:
759:
749:
730:
710:
690:
133:
123:
113:
11371:
10378:
10236:
10012:
9916:
7036:
6916:
6801:
6542:
6443:
5105:
1521:
981:
17427:
17290:
17242:
8333:
1531:
17417:
17407:
17280:
17270:
17232:
17222:
17012:
17002:
16992:
16964:
16954:
16944:
16743:
16733:
16723:
16695:
16685:
16675:
16580:
16570:
16560:
16432:
16422:
16412:
16308:
16298:
16288:
16147:
16137:
16127:
15903:
15893:
15883:
15803:
15793:
15783:
15647:
15637:
15627:
15379:
15369:
15359:
14859:
14849:
14839:
14667:
14657:
14647:
14439:
14429:
14419:
14171:
14161:
14151:
14002:
13992:
13982:
13840:
13830:
13820:
13755:
13745:
13735:
13710:
13700:
13690:
13657:
13647:
13637:
13609:
13536:
13526:
13516:
13415:
13405:
13395:
13367:
13349:
13339:
13329:
13120:
13110:
13100:
13012:
12993:
12983:
12973:
12440:
12430:
12420:
12392:
12374:
12364:
12354:
12278:
12268:
12258:
12103:
12084:
12074:
12064:
11575:
11565:
11555:
11527:
11509:
11499:
11489:
11342:
11323:
11313:
11303:
11129:
11111:
11101:
11091:
10935:
10925:
10915:
10869:
10859:
10849:
10831:
10803:
10793:
10783:
10755:
10737:
10727:
10717:
10330:
10301:
10291:
10281:
10080:
9994:
9984:
9974:
9898:
9888:
9878:
9279:
9269:
9259:
9118:
9108:
9098:
9079:
9069:
9059:
9031:
8553:
8543:
8533:
8505:
8487:
8477:
8467:
8353:
8343:
8177:
8138:
8117:
8107:
8097:
8078:
8068:
8058:
8039:
8029:
8019:
8000:
7990:
7980:
7387:
7377:
7367:
7339:
7311:
7265:
7255:
7245:
7217:
7199:
7189:
7179:
7151:
7133:
7123:
7113:
6643:
6633:
6623:
6482:
6472:
6462:
6240:
5956:
5923:
5890:
5857:
5824:
5791:
5758:
5725:
5674:
5641:
5580:
5527:
5494:
5461:
5428:
5406:
5396:
5386:
5357:
5267:
4979:
4969:
4959:
4936:
4926:
4916:
4893:
4883:
4873:
4850:
4840:
4830:
4808:
4779:
4769:
4759:
4717:
4707:
4697:
4674:
4664:
4654:
4630:
4620:
4610:
4587:
4577:
4567:
4544:
4534:
4524:
4501:
4491:
4481:
4459:
4449:
4439:
4357:
4347:
4337:
3920:
3868:
3858:
3829:
3819:
3772:
3762:
3733:
3723:
3676:
3666:
3637:
3627:
3598:
3588:
3492:
3464:
3454:
3415:
3397:
3387:
3377:
3354:
3344:
3334:
3263:
3245:
3235:
3225:
3202:
3192:
3182:
3154:
3139:
3106:
3088:
3078:
3068:
3045:
3035:
3025:
3002:
2992:
2982:
2896:
2857:
2847:
2818:
2808:
2779:
2769:
2740:
2730:
2701:
2691:
2662:
2652:
2450:
2440:
2310:
2292:
2282:
2272:
2239:
2221:
2211:
2201:
2092:
2074:
2064:
2054:
2021:
2003:
1993:
1983:
1955:
1940:
1912:
1897:
1864:
1846:
1836:
1826:
1793:
1775:
1765:
1755:
1511:
1488:
1473:
1426:
1411:
1356:
1346:
1336:
1295:
1280:
1246:
1236:
1226:
1144:
1134:
1124:
1082:
1072:
1062:
1034:
991:
971:
948:
933:
910:
900:
890:
816:
806:
796:
764:
754:
744:
715:
695:
128:
118:
108:
17585:(Chapter 21, Naming the Archimedean and Catalan polyhedra and tilings, Architectonic and Catoptric tessellations, p 292-298, includes all the nonprismatic forms)
9571:
can be orthogonally projected into the euclidean plane with various symmetry arrangements. The highest (hexagonal) symmetry form projects into a nonuniform
17658:(On the regular and semiregular nets of polyhedra and on the corresponding correlative nets), Mem. Società Italiana della Scienze, Ser.3, 14 (1905) 75–129.
13224:
A double symmetry construction can be made by placing truncated octahedra on the truncated cuboctahedra, resulting in a nonuniform honeycomb with
1567:
can be orthogonally projected into the euclidean plane with various symmetry arrangements. The highest (hexagonal) symmetry form projects into a
9158:
A double symmetry construction can be made by placing octahedra on the truncated cubes, resulting in a nonuniform honeycomb with two kinds of
14715:
Cells are irregular pyramids and can be seen as 1/24 of a cube, using one corner, one mid-edge point, two face centers, and the cube center.
8388:
A double symmetry construction can be made by placing octahedra on the cuboctahedra, resulting in a nonuniform honeycomb with two kinds of
4284:. A double symmetry construction can be constructed by placing a small cube into each large cube, resulting in a nonuniform honeycomb with
14732:
A double symmetry construction can be made by placing rhombicuboctahedra on the truncated cubes, resulting in a nonuniform honeycomb with
12290:
It has irregular triangle bipyramid cells which can be seen as 1/12 of a cube, made from the cube center, 2 face centers, and 2 vertices.
4047:
14453:
44:
16548:
is constructed by removing alternating long rectangles from the octagons orthogonally and is not uniform, but it can be represented as
14052:
A double symmetry construction can be made by placing icosahedra on the rhombicuboctahedra, resulting in a nonuniform honeycomb with
17478:
9536:
14605:, seen as boundary cells from a subset of cells. One has triangles and squares, and the other triangles, squares, and octagons.
377:
17635:
17582:
17696:
4370:
generates 15 permutations of uniform tessellations, 9 with distinct geometry including the alternated cubic honeycomb. The
16276:
is constructed by removing alternating long rectangles from the octagons and is not uniform, but it can be represented as
12801:
form can be drawn with one color for each cell type. The bifurcating diagram form can be drawn with two types (colors) of
17630:, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
6927:
4036:
4041:
4031:
5987:
5290:
generates 9 permutations of uniform tessellations, 4 with distinct geometry including the alternated cubic honeycomb.
17601:
18093:
18076:
12189:
A double symmetry construction can be made by placing cuboctahedra on the rhombicuboctahedra, which results in the
11180:
9544:
9432:
4267:
3908:
16004:
Individual cells have 2-fold rotational symmetry. In 2D orthogonal projection, this looks like a mirror symmetry.
4374:
cubic honeycomb (also known as the runcinated cubic honeycomb) is geometrically identical to the cubic honeycomb.
18514:
18152:
2418:
18587:
13856:
5975:
4726:
4683:
4026:
3442:
2189:
1971:
1743:
18572:
17613:(Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
5247:
2260:
2042:
18577:
18526:
13483:
15931:
15566:
11776:
11705:
9471:
7047:
6056:
5942:
5909:
5546:
5224:
4988:
4639:
457:
447:
17973:
17858:
17815:
17772:
17729:
18582:
17483:
14760:
14467:
14336:
11043:
9751:. These uniform symmetries can be represented by coloring differently the cells in each construction.
8397:
6368:
6030:
5660:
5447:
5051:
4183:
2874:
1814:
17937:
17901:
17394:
of the truncated square prismatic honeycomb, although it can not be made uniform, but it can be given
15255:
15217:
14971:
14679:
14276:
13548:
13132:
12870:
12830:
12538:
11993:
11953:
11665:
11003:
10189:
10121:
10025:
9929:
9831:
9743:. This honeycomb has four uniform constructions, with the truncated octahedral cells having different
9707:
9389:
8939:
8901:
8652:
7852:
7813:
7774:
7735:
7485:
6992:
6954:
6872:
6834:
6697:
6656:
6495:
6304:
6263:
6138:
5993:
212:
18308:
18253:
18204:
17638:
17488:
9572:
6761:
5876:
5843:
5810:
5313:
4596:
4553:
4397:
4295:
symmetry). Its vertex figure is a triangular pyramid with its lateral faces augmented by tetrahedra.
4256:
4245:
3846:
3807:
452:
438:
17357:
427:
Simple cubic lattices can be distorted into lower symmetries, represented by lower crystal systems:
18071:
17722:
17689:
17592:
17182:
17159:
16912:
16889:
16635:
16378:
16093:
15935:
15593:
14805:
14117:
13786:
13297:
13203:
12318:
11453:
11176:. These have symmetry , and respectively. The first and last symmetry can be doubled as ] and ].
11049:
10683:
9522:
9223:
8431:
7073:
442:
412:
369:
15473:
13210:
12700:
12158:
11821:, shown here with cubic symmetry, with atoms placed at the center of the cells of this honeycomb.
18103:
17493:
16882:
15817:
15495:
15194:
15053:
14875:
13488:
12802:
12640:
12456:
9580:
9576:
9491:
9166:(tetragonal disphenoids and digonal disphenoids). The vertex figure is an octakis square cupola.
6553:
5136:
4313:, two kinds of tetragonal disphenoids, triangular pyramids, and sphenoids. Its vertex figure has
3365:
3322:
3213:
3170:
1672:
16226:
14943:
14498:
13048:
12518:
10505:
9362:
17391:
17209:
16931:
16662:
15770:
of the omnitruncated cubic honeycomb, although it can not be made uniform, but it can be given
15767:
14767:
13259:
12669:
12598:
12243:
11818:
9693:
9552:
9246:
9137:
6402:
5693:
5513:
5480:
4945:
4902:
4309:
The resulting honeycomb can be alternated to produce another nonuniform honeycomb with regular
373:
317:
15525:
14079:
10987:
18552:
18545:
18538:
18360:
18298:
18243:
18194:
18132:
17570:
14370:
9499:
9347:
8239:
17094:
16495:
16248:
13677:
4280:
The cubic honeycomb has a lower symmetry as a runcinated cubic honeycomb, with two sizes of
18502:
18495:
18490:
17463:
17126:
16856:
15518:
15464:
15455:
15108:
can be orthogonally projected into the euclidean plane with various symmetry arrangements.
15049:
14948:
14778:
14516:
can be orthogonally projected into the euclidean plane with various symmetry arrangements.
14449:
14374:
13959:
13270:
13225:
13190:
12716:
can be orthogonally projected into the euclidean plane with various symmetry arrangements.
12644:
12636:
12465:
11836:
can be orthogonally projected into the euclidean plane with various symmetry arrangements.
11743:
10622:
10607:
10391:
9748:
9506:
9495:
9487:
9479:
9367:
9295:
8787:
can be orthogonally projected into the euclidean plane with various symmetry arrangements.
8731:
8232:
7714:
7624:
can be orthogonally projected into the euclidean plane with various symmetry arrangements.
7568:
4859:
4371:
462:
336:
297:
15536:
14090:
13912:
10519:
9678:
9671:
9664:
9657:
9650:
9170:
8:
18405:
18343:
18338:
18281:
18276:
18226:
18221:
18177:
18172:
18120:
17682:
17670:
16590:
16448:
16318:
16163:
15989:
15713:
14733:
14394:
14378:
14258:
14187:
14012:
11747:
11591:
10512:
9697:
8321:
8309:
7597:
7526:
397:
54:
16524:
17566:
17152:
16875:
15443:
15078:
15070:
15061:
15011:
14939:
14928:
14602:
14459:
14397:
14317:
14261:
12661:
12579:
11768:
11641:
10656:
9701:
9556:
9528:
9358:
9328:
8752:
8629:
7589:
7462:
4299:
416:
365:
325:
255:
189:
17656:
Sulle reti di poliedri regolari e semiregolari e sulle corrispondenti reti correlative
17617:
17189:
16919:
16642:
16385:
16100:
15856:
15600:
15424:
14812:
14253:
14124:
13934:
13793:
13304:
13041:
12513:
12325:
11460:
10690:
9230:
9181:
8438:
7080:
4218:
4100:
4093:
4086:
3566:
3559:
3552:
2623:
2616:
2609:
1664:
859:
401:
321:
85:
18350:
18288:
18233:
18184:
18162:
18142:
18024:
17710:
17706:
17631:
17597:
17578:
17377:
17130:
17105:
16860:
16835:
16535:
16259:
15920:
15749:
15439:
15417:
15028:
14923:
14598:
14353:
13945:
13559:
13186:
12652:
12615:
12523:
12197:, square antiprism pairs and zero-height tetragonal disphenoids as components of the
11722:
11060:
9638:
9631:
9624:
9617:
9610:
9518:
9483:
9449:
9310:
8710:
8317:
7543:
4234:
4161:
3750:
2911:
2796:
1568:
1446:
1385:
301:
276:
272:
17663:
17556:
14583:
14576:
14569:
12783:
12776:
12769:
10491:
9342:
18125:
18061:
17651:
17447:
17365:
17316:
17138:
17047:
16348:
16194:
15946:
15821:
15726:
15672:
15551:
15546:
This honeycomb can then be alternated to produce another nonuniform honeycomb with
15210:
15175:
15168:
15161:
14745:
14557:
14550:
14543:
14061:
14034:
13878:
13237:
12757:
12750:
12743:
12295:
12222:
12206:
12151:
11918:
11759:
11711:
11630:
11625:
10628:
This honeycomb can then be alternated to produce another nonuniform honeycomb with
10498:
8869:
8393:
8367:
8246:
7727:
7706:
6063:
4172:
4150:
3986:
2945:
2835:
2757:
1713:
1676:
845:
836:
629:
381:
17145:
15149:
15142:
15135:
14720:
14342:
13722:
13251:(as tetragonal disphenoids). Its vertex figure is topologically equivalent to the
12952:
12287:, containing faces from two of four hyperplanes of the cubic fundamental domain.
8404:
17499:
17451:
17395:
16864:
16769:
16549:
16399:
16277:
16114:
15969:
15870:
15825:
15771:
15614:
15541:
15503:
15499:
15346:
15338:
15331:
15198:
15190:
15057:
14884:
14826:
14783:
14636:
14491:
14407:
14386:
14205:
14138:
14095:
13971:
13807:
13598:
13316:
13275:
13229:
13088:
12960:
12945:
12798:
12341:
12247:
12051:
11903:
11896:
11889:
11476:
11271:
11183:. The centers of the icosahedra are located at the fcc positions of the lattice.
11079:
10704:
10611:
10249:
9514:
9510:
9453:
9186:
9144:
9018:
8612:
8454:
8409:
8225:
7965:
7718:
7547:
7446:
7100:
4304:
2940:
2918:
1708:
854:
669:
95:
12217:(as tetragonal disphenoids), with a vertex figure topologically equivalent to a
11877:
11870:
11863:
6424:
2581:
18392:
18385:
18378:
18325:
18318:
18263:
18019:
17621:
14759:(as digonal disphenoids). Its vertex figure is topologically equivalent to the
14382:
14196:
14072:
13173:
12604:
12137:
10592:
10585:
10578:
10564:
8854:
8847:
8840:
8743:
8735:
8618:
8569:
7691:
7684:
7677:
4058:
3706:
3524:
474:
433:
351:, so that there are no gaps. It is an example of the more general mathematical
14477:
12677:
12130:
11805:
10571:
8828:
8821:
8814:
7665:
7658:
7651:
6782:
6099:
18566:
18051:
18041:
18031:
17532:
17075:
16806:
16604:: square prisms and rectangular trapezoprisms (topologically equivalent to a
16509:
16489:
16336:: square prisms and rectangular trapezoprisms (topologically equivalent to a
16234:
16180:
15667:
15571:
15530:
15411:
15086:
15064:
14963:
14917:
14879:
14772:
14400:
14268:
14247:
14084:
13920:
13906:
13873:
13496:
13477:
13444:
13435:
13264:
13035:
12822:
12655:
12530:
12507:
12460:
12202:
12198:
12145:
11945:
11922:
11762:
11751:
11657:
11600:
11252:
10995:
10964:
10485:
10477:
10471:
10462:
10456:
10450:
10444:
10435:
9824:
9744:
9740:
9502:
9382:
9336:
9175:
9131:
9003:
8893:
8873:
8746:
8645:
8606:
8219:
7957:
7950:
7943:
7710:
7583:
7576:
7478:
7440:
7403:
6575:
6026:
5287:
4367:
3574:
1686:
1572:
1315:
1163:
493:
405:
309:
308:
cells. It has 4 cubes around every edge, and 8 cubes around each vertex. Its
250:
205:
167:
16456:
16171:
15718:
15562:(as tetragonal disphenoids, phyllic disphenoids, and irregular tetrahedra).
14200:
14191:
13864:
12469:
11595:
10429:
10423:
10414:
10408:
10399:
9438:
9299:
9010:
8573:
8375:
7936:
4240:
3802:
17329:
17122:
16852:
15685:
15045:
15017:
13595:(as tetragonal disphenoids), and new tetrahedral cells created at the gaps.
13453:
12632:
11784:
11739:
11604:
10955:
9475:
9466:
The bitruncated cubic honeycomb shown here in relation to a cubic honeycomb
9206:
8727:
8582:
7580:
7564:
7451:
7416:
7407:
4139:
2718:
385:
357:
293:
148:
7709:
for the cells of this honeycomb with reflective symmetry, listed by their
1546:
1097:
1006:
33:
17455:
17325:
15939:
15829:
15681:
15559:
15293:
14935:
14756:
14313:
14053:
14023:
13869:
13592:
13581:
13449:
13440:
13248:
12907:
12575:
12214:
12030:
11637:
11192:
10960:
10951:
10637:
10629:
9760:
9548:
9354:
9323:
9163:
8978:
8767:
8760:
8693:
8625:
7889:
7604:
7532:
7458:
6044:
5301:
4385:
4310:
4223:
4201:
4117:
3711:
3615:
2640:
849:
591:
505:
185:
15997:
14610:
16501:
15555:
15480:
14737:
14615:
14057:
13252:
12210:
12194:
10633:
9159:
8739:
8699:
8578:
8389:
7572:
7412:
4229:
4212:
4207:
4145:
3745:
3654:
3649:
2752:
1683:
1657:
344:
313:
178:
173:
11925:, the second seen with alternately colored rhombicuboctahedral cells.
8392:(regular octahedra and triangular antiprisms). The vertex figure is a
16329:
16176:
15813:
15663:
15547:
15314:
13963:
13577:
13431:
12928:
11230:
10652:
9802:
6051:
5308:
4392:
4079:
3013:
2602:
1660:
1642:
1635:
1628:
469:
16824:
16067:
16060:
16053:
16046:
16037:
16030:
4156:
2791:
1616:
1609:
1602:
261:
17340:
17320:
17062:
17051:
17042:
16782:
16476:
16465:
16209:
16198:
16189:
15696:
15676:
14229:
14218:
13893:
13882:
13464:
12478:
11613:
10975:
10660:
10648:
8593:
7427:
6192:
4072:
3978:
3545:
3538:
2935:
2595:
1703:
16773:
15739:
14888:
14484:
14209:
8876:, the second seen with alternately colored truncated cubic cells.
4262:
4065:
3903:
3531:
2588:
28:
17588:
16798:
16014:
14909:
14904:
14239:
12499:
12494:
9315:
8598:
8313:
6029:. The symmetry can be multiplied by the symmetry of rings in the
4320:
symmetry and has 26 triangular faces, 39 edges, and 15 vertices.
15835:
13970:(square prisms). It is not uniform but it can be represented as
13597:
Although it is not uniform, constructionally it can be given as
4251:
3841:
17345:
17067:
16793:
16481:
16214:
15701:
14899:
14234:
13898:
13469:
12489:
9462:
9162:(regular octahedra and triangular antiprisms) and two kinds of
7432:
4134:
4016:
2713:
576:
562:
486:
480:
159:
13129:. This honeycomb cells represents the fundamental domains of
12683:
11789:
4196:
4178:
4167:
4112:
3610:
2869:
2830:
2635:
17504:
16023:
15982:
15959:
14448:
with three ringed nodes representing 3 active mirrors in the
11812:
4123:
2674:
569:
555:
15981:
is a space-filling honeycomb constructed as the dual of the
15092:
13281:
4288:, square prisms, and rectangular trapezoprisms (a cube with
17459:
17134:
17038:
16868:
16778:
16605:
16601:
16461:
16337:
16333:
16185:
15577:
15507:
14741:
14390:
14214:
13967:
13233:
12797:
Cells can be shown in two different symmetries. The linear
12648:
12474:
12218:
11755:
11609:
8772:
7609:
4285:
4281:
4128:
2915:
2679:
498:
305:
144:
17535:
9204:
26:
10667:
16077:
15517:-symmetric variants). Its vertex figure is an irregular
11179:
This honeycomb is represented in the boron atoms of the
9551:
can not tessellate space alone, this dual has identical
9212:
583:
16619:
17166:
10614:(as ditrigonal trapezoprisms). Its vertex figure is a
422:
17976:
17940:
17904:
17861:
17818:
17775:
17732:
15258:
15220:
14974:
14682:
14279:
13135:
12873:
12833:
12541:
12193:, by taking the triangular antiprism gaps as regular
11996:
11956:
11668:
11006:
10192:
10124:
10028:
9932:
9834:
9710:
9575:. A square symmetry projection forms two overlapping
9392:
8942:
8904:
8655:
7855:
7816:
7777:
7738:
7488:
6995:
6957:
6875:
6837:
6700:
6659:
6498:
6307:
6266:
6141:
5996:
1682:
It is in a sequence of polychora and honeycombs with
215:
15189:
Cells can be shown in two different symmetries. The
839:, derived from different symmetries. These include:
13180:
9517:, with 2 hexagons and one square on each edge, and
1651:
16:
Only regular space-filling tessellation of the cube
18004:
17962:
17926:
17889:
17846:
17803:
17760:
17628:Kaleidoscopes: Selected Writings of H.S.M. Coxeter
17496:A hyperbolic cubic honeycomb with 5 cubes per edge
16896:
15280:
15242:
14996:
14704:
14301:
13157:
12895:
12855:
12563:
12018:
11978:
11690:
11028:
10214:
10146:
10050:
9954:
9856:
9732:
9414:
8964:
8926:
8677:
7877:
7838:
7799:
7760:
7510:
7017:
6979:
6897:
6859:
6722:
6681:
6520:
6329:
6288:
6163:
6018:
4323:
237:
14101:
12302:
1671:cubes around each edge. It's also related to the
18564:
15506:(as ditrigonal trapezoprisms), and two kinds of
14789:
388:to form a uniform honeycomb in spherical space.
15558:(as triangular antiprisms), and three kinds of
1667:{4,3,3}, which exists in 4-space, and only has
364:Honeycombs are usually constructed in ordinary
16362:
15988:24 cells fit around a vertex, making a chiral
15843:Dual alternated omnitruncated cubic honeycomb
13770:
12229:
12190:
11437:
9192:
17690:
17664:"3D Euclidean Honeycombs x4o3o4o - chon - O1"
15979:dual alternated omnitruncated cubic honeycomb
15836:Dual alternated omnitruncated cubic honeycomb
15740:Dual alternated omnitruncated cubic honeycomb
14676:. Faces exist in 3 of 4 hyperplanes of the ,
14622:
404:of the form {4,3,...,3,4}, starting with the
14592:
8415:
7057:
17173:
16903:
16626:
16369:
16084:
15842:
15584:
15052:) in Euclidean 3-space. It is composed of
14796:
14377:) in Euclidean 3-space. It is composed of
14108:
13777:
13288:
12309:
11746:) in Euclidean 3-space. It is composed of
11444:
10674:
9199:
8734:) in Euclidean 3-space. It is composed of
8422:
7571:) in Euclidean 3-space. It is composed of
7064:
396:It is part of a multidimensional family of
21:
17697:
17683:
17170:
16900:
16623:
16366:
16081:
15839:
15581:
14793:
14105:
13774:
13289:Alternated cantitruncated cubic honeycomb
13285:
12306:
11441:
10671:
9692:The vertex figure for this honeycomb is a
9196:
8419:
8316:centers of the cuboctahedra, creating two
7061:
18:
17604:p. 296, Table II: Regular honeycombs
15992:that can be stacked in all 3-dimensions:
15585:Alternated omnitruncated cubic honeycomb
13570:alternated cantitruncated cubic honeycomb
13282:Alternated cantitruncated cubic honeycomb
13074:
503:
292:is the only proper regular space-filling
17479:Architectonic and catoptric tessellation
15983:alternated omnitruncated cubic honeycomb
15960:Alternated omnitruncated cubic honeycomb
15760:alternated omnitruncated cubic honeycomb
15578:Alternated omnitruncated cubic honeycomb
15510:(as rectangular trapezoprisms and their
9537:Architectonic and catoptric tessellation
9461:
17538:6-1 cases, skipping one with zero marks
16274:runcic cantitruncated cubic cellulation
10675:Alternated bitruncated cubic honeycomb
1571:. A square symmetry projection forms a
18565:
17671:Uniform Honeycombs in 3-Space: 01-Chon
17596:, (3rd edition, 1973), Dover edition,
16085:Runcic cantitruncated cubic honeycomb
15489:
14727:
14047:
13219:
12184:
11071:alternated bitruncated cubic honeycomb
10668:Alternated bitruncated cubic honeycomb
10640:(as sphenoids). Its vertex figure has
10601:
9153:
8383:
17458:(as tetragonal disphenoids) from the
16627:Truncated square prismatic honeycomb
16270:runcic cantitruncated cubic honeycomb
16078:Runcic cantitruncated cubic honeycomb
12695:Four cells exist around each vertex:
12225:attached to one of its square faces.
8742:in a ratio of 1:1, with an isosceles
391:
17661:
17644:Regular and Semi Regular Polytopes I
17174:Snub square antiprismatic honeycomb
17089:Cairo pentagonal prismatic honeycomb
16845:truncated square prismatic honeycomb
16620:Truncated square prismatic honeycomb
16358:-symmetry wedges) filling the gaps.
15433:
14044:-symmetry wedges) filling the gaps.
10659:(divided into two sets of 2), and 4
4275:
830:
17547:Williams, 1979, p 199, Figure 5-38.
17388:snub square antiprismatic honeycomb
17167:Snub square antiprismatic honeycomb
12639:) in Euclidean 3-space, made up of
423:Isometries of simple cubic lattices
13:
18005:{\displaystyle {\tilde {E}}_{n-1}}
17890:{\displaystyle {\tilde {D}}_{n-1}}
17847:{\displaystyle {\tilde {B}}_{n-1}}
17804:{\displaystyle {\tilde {C}}_{n-1}}
17761:{\displaystyle {\tilde {A}}_{n-1}}
15851:Dual alternated uniform honeycomb
8324:is represented by Coxeter diagram
372:. They may also be constructed in
14:
18599:
17119:simo-square prismatic cellulation
16849:tomo-square prismatic cellulation
14744:(as square prisms), two kinds of
12213:(as triangular antipodiums), and
11929:Vertex uniform colorings by cell
11078:constructions from three related
8308:This honeycomb can be divided on
1542:t{∞}×t{∞}×t{∞}
17963:{\displaystyle {\tilde {F}}_{4}}
17927:{\displaystyle {\tilde {G}}_{2}}
17440:
17435:
17430:
17425:
17420:
17415:
17410:
17405:
17400:
17356:
17328:
17319:
17303:
17298:
17293:
17288:
17283:
17278:
17273:
17268:
17263:
17255:
17250:
17245:
17240:
17235:
17230:
17225:
17220:
17215:
17144:
17093:
17050:
17041:
17025:
17020:
17015:
17010:
17005:
17000:
16995:
16990:
16985:
16977:
16972:
16967:
16962:
16957:
16952:
16947:
16942:
16937:
16904:Snub square prismatic honeycomb
16874:
16823:
16819:Tetrakis square prismatic tiling
16781:
16772:
16756:
16751:
16746:
16741:
16736:
16731:
16726:
16721:
16716:
16708:
16703:
16698:
16693:
16688:
16683:
16678:
16673:
16668:
16583:
16578:
16573:
16568:
16563:
16558:
16553:
16523:
16494:
16464:
16455:
16435:
16430:
16425:
16420:
16415:
16410:
16405:
16311:
16306:
16301:
16296:
16291:
16286:
16281:
16247:
16225:
16197:
16188:
16179:
16170:
16150:
16145:
16140:
16135:
16130:
16125:
16120:
16066:
16059:
16052:
16045:
16036:
16029:
16022:
16013:
15996:
15919:
15906:
15901:
15896:
15891:
15886:
15881:
15876:
15806:
15801:
15796:
15791:
15786:
15781:
15776:
15717:
15712:
15684:
15675:
15666:
15650:
15645:
15640:
15635:
15630:
15625:
15620:
15565:
15535:
15524:
15479:
15472:
15463:
15454:
15423:
15416:
15401:
15396:
15391:
15382:
15377:
15372:
15367:
15362:
15357:
15352:
15337:
15330:
15281:{\displaystyle {\tilde {C}}_{3}}
15243:{\displaystyle {\tilde {C}}_{3}}
15174:
15167:
15160:
15148:
15141:
15134:
15099:
15091:
15085:
15016:
14997:{\displaystyle {\tilde {C}}_{3}}
14922:
14887:
14878:
14862:
14857:
14852:
14847:
14842:
14837:
14832:
14777:
14766:
14719:
14705:{\displaystyle {\tilde {C}}_{3}}
14670:
14665:
14660:
14655:
14650:
14645:
14640:
14614:
14609:
14582:
14575:
14568:
14556:
14549:
14542:
14507:
14497:
14490:
14483:
14476:
14442:
14437:
14432:
14427:
14422:
14417:
14412:
14367:runcitruncated cubic cellulation
14341:
14302:{\displaystyle {\tilde {C}}_{3}}
14252:
14217:
14208:
14199:
14190:
14174:
14169:
14164:
14159:
14154:
14149:
14144:
14089:
14078:
14005:
14000:
13995:
13990:
13985:
13980:
13975:
13933:
13911:
13881:
13872:
13863:
13843:
13838:
13833:
13828:
13823:
13818:
13813:
13758:
13753:
13748:
13743:
13738:
13733:
13728:
13721:
13713:
13708:
13703:
13698:
13693:
13688:
13683:
13676:
13660:
13655:
13650:
13645:
13640:
13635:
13630:
13622:
13617:
13612:
13607:
13602:
13547:
13539:
13534:
13529:
13524:
13519:
13514:
13509:
13487:
13482:
13452:
13443:
13434:
13418:
13413:
13408:
13403:
13398:
13393:
13388:
13380:
13375:
13370:
13365:
13360:
13352:
13347:
13342:
13337:
13332:
13327:
13322:
13269:
13258:
13209:
13202:
13181:Related polyhedra and honeycombs
13172:
13158:{\displaystyle {\tilde {B}}_{3}}
13123:
13118:
13113:
13108:
13103:
13098:
13093:
13047:
13040:
13025:
13020:
13015:
13010:
13005:
12996:
12991:
12986:
12981:
12976:
12971:
12966:
12951:
12944:
12896:{\displaystyle {\tilde {B}}_{3}}
12856:{\displaystyle {\tilde {C}}_{3}}
12782:
12775:
12768:
12756:
12749:
12742:
12707:
12699:
12682:
12676:
12629:cantitruncated cubic cellulation
12603:
12564:{\displaystyle {\tilde {C}}_{3}}
12517:
12512:
12477:
12468:
12459:
12443:
12438:
12433:
12428:
12423:
12418:
12413:
12405:
12400:
12395:
12390:
12385:
12377:
12372:
12367:
12362:
12357:
12352:
12347:
12294:
12281:
12276:
12271:
12266:
12261:
12256:
12251:
12157:
12150:
12136:
12129:
12116:
12111:
12106:
12101:
12096:
12087:
12082:
12077:
12072:
12067:
12062:
12057:
12019:{\displaystyle {\tilde {B}}_{3}}
11979:{\displaystyle {\tilde {C}}_{3}}
11921:by reflectional symmetry of the
11902:
11895:
11888:
11876:
11869:
11862:
11827:
11811:
11804:
11788:
11783:
11710:
11691:{\displaystyle {\tilde {C}}_{3}}
11624:
11612:
11603:
11594:
11578:
11573:
11568:
11563:
11558:
11553:
11548:
11540:
11535:
11530:
11525:
11520:
11512:
11507:
11502:
11497:
11492:
11487:
11482:
11403:
11398:
11393:
11388:
11383:
11374:
11369:
11364:
11355:
11350:
11345:
11340:
11335:
11326:
11321:
11316:
11311:
11306:
11301:
11296:
11287:
11282:
11277:
11170:
11165:
11160:
11155:
11150:
11142:
11137:
11132:
11127:
11122:
11114:
11109:
11104:
11099:
11094:
11089:
11084:
11048:
11029:{\displaystyle {\tilde {C}}_{3}}
10986:
10963:
10954:
10938:
10933:
10928:
10923:
10918:
10913:
10908:
10900:
10895:
10890:
10885:
10880:
10872:
10867:
10862:
10857:
10852:
10847:
10842:
10834:
10829:
10824:
10819:
10814:
10806:
10801:
10796:
10791:
10786:
10781:
10776:
10768:
10763:
10758:
10753:
10748:
10740:
10735:
10730:
10725:
10720:
10715:
10710:
10636:(as triangular antiprisms), and
10591:
10584:
10577:
10570:
10563:
10518:
10511:
10504:
10497:
10490:
10476:
10470:
10461:
10455:
10449:
10443:
10434:
10428:
10422:
10413:
10407:
10398:
10381:
10376:
10371:
10362:
10357:
10352:
10347:
10342:
10333:
10328:
10323:
10318:
10313:
10304:
10299:
10294:
10289:
10284:
10279:
10274:
10265:
10260:
10255:
10239:
10234:
10229:
10215:{\displaystyle {\tilde {A}}_{3}}
10179:
10174:
10169:
10164:
10159:
10147:{\displaystyle {\tilde {A}}_{3}}
10111:
10106:
10101:
10096:
10091:
10083:
10078:
10073:
10068:
10063:
10051:{\displaystyle {\tilde {B}}_{3}}
10015:
10010:
10005:
9997:
9992:
9987:
9982:
9977:
9972:
9967:
9955:{\displaystyle {\tilde {C}}_{3}}
9919:
9914:
9909:
9901:
9896:
9891:
9886:
9881:
9876:
9871:
9857:{\displaystyle {\tilde {C}}_{3}}
9733:{\displaystyle {\tilde {A}}_{3}}
9677:
9670:
9663:
9656:
9649:
9637:
9630:
9623:
9616:
9609:
9562:
9545:disphenoid tetrahedral honeycomb
9437:
9433:Disphenoid tetrahedral honeycomb
9415:{\displaystyle {\tilde {C}}_{3}}
9341:
9298:
9282:
9277:
9272:
9267:
9262:
9257:
9252:
9211:
9205:
9180:
9169:
9143:
9136:
9121:
9116:
9111:
9106:
9101:
9096:
9091:
9082:
9077:
9072:
9067:
9062:
9057:
9052:
9044:
9039:
9034:
9029:
9024:
9009:
9002:
8965:{\displaystyle {\tilde {C}}_{3}}
8927:{\displaystyle {\tilde {B}}_{3}}
8872:by reflectional symmetry of the
8853:
8846:
8839:
8827:
8820:
8813:
8778:
8771:
8766:
8698:
8678:{\displaystyle {\tilde {C}}_{3}}
8611:
8581:
8572:
8556:
8551:
8546:
8541:
8536:
8531:
8526:
8518:
8513:
8508:
8503:
8498:
8490:
8485:
8480:
8475:
8470:
8465:
8460:
8403:
8374:
8356:
8351:
8346:
8341:
8336:
8331:
8326:
8245:
8238:
8231:
8224:
8209:
8204:
8199:
8194:
8189:
8180:
8175:
8170:
8165:
8160:
8151:
8146:
8141:
8136:
8131:
8120:
8115:
8110:
8105:
8100:
8095:
8090:
8081:
8076:
8071:
8066:
8061:
8056:
8051:
8042:
8037:
8032:
8027:
8022:
8017:
8012:
8003:
7998:
7993:
7988:
7983:
7978:
7973:
7956:
7949:
7942:
7935:
7878:{\displaystyle {\tilde {A}}_{3}}
7839:{\displaystyle {\tilde {B}}_{3}}
7800:{\displaystyle {\tilde {B}}_{3}}
7761:{\displaystyle {\tilde {C}}_{3}}
7690:
7683:
7676:
7664:
7657:
7650:
7615:
7608:
7603:
7531:
7511:{\displaystyle {\tilde {C}}_{3}}
7445:
7415:
7406:
7390:
7385:
7380:
7375:
7370:
7365:
7360:
7352:
7347:
7342:
7337:
7332:
7324:
7319:
7314:
7309:
7304:
7296:
7291:
7286:
7281:
7276:
7268:
7263:
7258:
7253:
7248:
7243:
7238:
7230:
7225:
7220:
7215:
7210:
7202:
7197:
7192:
7187:
7182:
7177:
7172:
7164:
7159:
7154:
7149:
7144:
7136:
7131:
7126:
7121:
7116:
7111:
7106:
7039:
7034:
7029:
7018:{\displaystyle {\tilde {C}}_{3}}
6980:{\displaystyle {\tilde {A}}_{3}}
6919:
6914:
6909:
6898:{\displaystyle {\tilde {C}}_{3}}
6860:{\displaystyle {\tilde {A}}_{3}}
6823:
6818:
6813:
6804:
6799:
6794:
6781:
6753:
6748:
6743:
6738:
6733:
6723:{\displaystyle {\tilde {C}}_{3}}
6682:{\displaystyle {\tilde {A}}_{3}}
6646:
6641:
6636:
6631:
6626:
6621:
6616:
6607:
6602:
6597:
6592:
6587:
6574:
6545:
6540:
6535:
6521:{\displaystyle {\tilde {A}}_{3}}
6485:
6480:
6475:
6470:
6465:
6460:
6455:
6446:
6441:
6436:
6423:
6394:
6389:
6384:
6379:
6374:
6360:
6355:
6350:
6345:
6340:
6330:{\displaystyle {\tilde {B}}_{3}}
6289:{\displaystyle {\tilde {A}}_{3}}
6253:
6248:
6243:
6238:
6233:
6224:
6219:
6214:
6209:
6204:
6191:
6164:{\displaystyle {\tilde {A}}_{3}}
6128:
6123:
6118:
6113:
6108:
6098:
6019:{\displaystyle {\tilde {A}}_{3}}
5988:five distinct uniform honeycombs
5969:
5964:
5959:
5954:
5949:
5936:
5931:
5926:
5921:
5916:
5903:
5898:
5893:
5888:
5883:
5870:
5865:
5860:
5855:
5850:
5837:
5832:
5827:
5822:
5817:
5804:
5799:
5794:
5789:
5784:
5771:
5766:
5761:
5756:
5751:
5738:
5733:
5728:
5723:
5718:
5687:
5682:
5677:
5672:
5667:
5654:
5649:
5644:
5639:
5634:
5622:
5617:
5612:
5607:
5602:
5593:
5588:
5583:
5578:
5573:
5540:
5535:
5530:
5525:
5520:
5507:
5502:
5497:
5492:
5487:
5474:
5469:
5464:
5459:
5454:
5441:
5436:
5431:
5426:
5421:
5409:
5404:
5399:
5394:
5389:
5384:
5379:
5370:
5365:
5360:
5355:
5350:
5280:
5275:
5270:
5265:
5260:
5241:
5236:
5231:
5218:
5213:
5208:
5195:
5190:
5185:
5172:
5167:
5162:
5130:
5125:
5120:
5108:
5103:
5098:
5089:
5084:
5079:
5045:
5040:
5035:
5023:
5018:
5013:
4982:
4977:
4972:
4967:
4962:
4957:
4952:
4939:
4934:
4929:
4924:
4919:
4914:
4909:
4896:
4891:
4886:
4881:
4876:
4871:
4866:
4853:
4848:
4843:
4838:
4833:
4828:
4823:
4811:
4806:
4801:
4796:
4791:
4782:
4777:
4772:
4767:
4762:
4757:
4752:
4720:
4715:
4710:
4705:
4700:
4695:
4690:
4677:
4672:
4667:
4662:
4657:
4652:
4647:
4633:
4628:
4623:
4618:
4613:
4608:
4603:
4590:
4585:
4580:
4575:
4570:
4565:
4560:
4547:
4542:
4537:
4532:
4527:
4522:
4517:
4504:
4499:
4494:
4489:
4484:
4479:
4474:
4462:
4457:
4452:
4447:
4442:
4437:
4432:
4360:
4355:
4350:
4345:
4340:
4335:
4330:
4298:
4261:
4250:
4239:
4228:
4217:
4206:
4195:
4177:
4166:
4155:
4144:
4133:
4122:
4111:
4099:
4092:
4085:
4078:
4071:
4064:
4057:
3956:
3951:
3946:
3941:
3933:
3928:
3923:
3918:
3913:
3902:
3894:
3889:
3884:
3879:
3871:
3866:
3861:
3856:
3851:
3840:
3832:
3827:
3822:
3817:
3812:
3801:
3793:
3788:
3783:
3775:
3770:
3765:
3760:
3755:
3744:
3736:
3731:
3726:
3721:
3716:
3705:
3697:
3692:
3687:
3679:
3674:
3669:
3664:
3659:
3648:
3640:
3635:
3630:
3625:
3620:
3609:
3601:
3596:
3591:
3586:
3581:
3565:
3558:
3551:
3544:
3537:
3530:
3523:
3510:
3505:
3500:
3495:
3490:
3485:
3477:
3472:
3467:
3462:
3457:
3452:
3447:
3433:
3428:
3423:
3418:
3413:
3408:
3400:
3395:
3390:
3385:
3380:
3375:
3370:
3357:
3352:
3347:
3342:
3337:
3332:
3327:
3314:
3309:
3304:
3299:
3294:
3289:
3284:
3276:
3271:
3266:
3261:
3256:
3248:
3243:
3238:
3233:
3228:
3223:
3218:
3205:
3200:
3195:
3190:
3185:
3180:
3175:
3162:
3157:
3152:
3147:
3142:
3137:
3132:
3127:
3119:
3114:
3109:
3104:
3099:
3091:
3086:
3081:
3076:
3071:
3066:
3061:
3048:
3043:
3038:
3033:
3028:
3023:
3018:
3005:
3000:
2995:
2990:
2985:
2980:
2975:
2899:
2894:
2889:
2884:
2879:
2868:
2860:
2855:
2850:
2845:
2840:
2829:
2821:
2816:
2811:
2806:
2801:
2790:
2782:
2777:
2772:
2767:
2762:
2751:
2743:
2738:
2733:
2728:
2723:
2712:
2704:
2699:
2694:
2689:
2684:
2673:
2665:
2660:
2655:
2650:
2645:
2634:
2622:
2615:
2608:
2601:
2594:
2587:
2580:
2567:
2562:
2557:
2552:
2547:
2542:
2537:
2532:
2524:
2519:
2514:
2509:
2504:
2499:
2494:
2489:
2481:
2476:
2471:
2466:
2461:
2453:
2448:
2443:
2438:
2433:
2428:
2423:
2409:
2404:
2399:
2394:
2389:
2384:
2379:
2374:
2366:
2361:
2356:
2351:
2346:
2341:
2336:
2331:
2323:
2318:
2313:
2308:
2303:
2295:
2290:
2285:
2280:
2275:
2270:
2265:
2252:
2247:
2242:
2237:
2232:
2224:
2219:
2214:
2209:
2204:
2199:
2194:
2181:
2176:
2171:
2166:
2161:
2156:
2151:
2143:
2138:
2133:
2128:
2123:
2118:
2113:
2105:
2100:
2095:
2090:
2085:
2077:
2072:
2067:
2062:
2057:
2052:
2047:
2034:
2029:
2024:
2019:
2014:
2006:
2001:
1996:
1991:
1986:
1981:
1976:
1963:
1958:
1953:
1948:
1943:
1938:
1933:
1928:
1920:
1915:
1910:
1905:
1900:
1895:
1890:
1885:
1877:
1872:
1867:
1862:
1857:
1849:
1844:
1839:
1834:
1829:
1824:
1819:
1806:
1801:
1796:
1791:
1786:
1778:
1773:
1768:
1763:
1758:
1753:
1748:
1652:Related polytopes and honeycombs
1641:
1634:
1627:
1615:
1608:
1601:
1545:
1534:
1529:
1524:
1519:
1514:
1509:
1504:
1496:
1491:
1486:
1481:
1476:
1471:
1466:
1461:
1445:
1442:t{∞}×t{∞}×{∞}
1434:
1429:
1424:
1419:
1414:
1409:
1404:
1399:
1384:
1369:
1364:
1359:
1354:
1349:
1344:
1339:
1334:
1329:
1314:
1303:
1298:
1293:
1288:
1283:
1278:
1273:
1268:
1259:
1254:
1249:
1244:
1239:
1234:
1229:
1224:
1219:
1194:
1189:
1184:
1162:
1147:
1142:
1137:
1132:
1127:
1122:
1117:
1096:
1085:
1080:
1075:
1070:
1065:
1060:
1055:
1047:
1042:
1037:
1032:
1027:
1005:
994:
989:
984:
979:
974:
969:
964:
956:
951:
946:
941:
936:
931:
926:
921:
913:
908:
903:
898:
893:
888:
883:
819:
814:
809:
804:
799:
794:
789:
777:
772:
767:
762:
757:
752:
747:
742:
737:
728:
723:
718:
713:
708:
703:
698:
693:
688:
683:
678:
582:
575:
568:
561:
554:
260:
238:{\displaystyle {\tilde {C}}_{3}}
172:
147:
131:
126:
121:
116:
111:
106:
101:
32:
27:
17646:, (1.9 Uniform space-fillings)
17373:
17364:
17352:
17336:
17312:
17208:
17188:
17178:
17115:snub square prismatic honeycomb
17101:
17084:
17074:
17058:
17034:
16930:
16918:
16908:
16897:Snub square prismatic honeycomb
16831:
16814:
16805:
16789:
16765:
16661:
16641:
16631:
16531:
16518:
16508:
16488:
16472:
16444:
16398:
16384:
16374:
16255:
16242:
16233:
16221:
16205:
16159:
16113:
16099:
16089:
15965:
15955:
15945:
15927:
15915:
15869:
15855:
15847:
15745:
15735:
15725:
15708:
15692:
15659:
15613:
15599:
15589:
15042:omnitruncated cubic cellulation
15024:
15007:
14962:
14934:
14916:
14895:
14871:
14825:
14811:
14801:
14393:in a ratio of 1:1:3:3, with an
14349:
14332:
14312:
14267:
14246:
14225:
14183:
14137:
14123:
14113:
14109:Runcitruncated cubic honeycomb
13958:is constructed by snubbing the
13941:
13928:
13919:
13905:
13889:
13852:
13806:
13792:
13782:
13576:contains three types of cells:
13555:
13504:
13495:
13476:
13460:
13427:
13315:
13303:
13293:
13232:(as ditrigonal trapezoprisms),
12611:
12594:
12574:
12529:
12506:
12485:
12452:
12340:
12324:
12314:
12310:Cantitruncated cubic honeycomb
11718:
11701:
11656:
11636:
11620:
11587:
11475:
11459:
11449:
11056:
11039:
10994:
10982:
10971:
10947:
10703:
10689:
10679:
9755:Five uniform colorings by cell
9445:
9426:
9381:
9353:
9335:
9322:
9306:
9291:
9245:
9229:
9219:
8706:
8689:
8644:
8624:
8605:
8589:
8565:
8453:
8437:
8427:
7539:
7522:
7477:
7457:
7439:
7423:
7399:
7099:
7079:
7069:
4324:Related Euclidean tessellations
1679:with 5 cubes around each edge.
268:
249:
204:
184:
166:
155:
140:
94:
84:
60:
50:
40:
17984:
17948:
17912:
17869:
17826:
17783:
17740:
17620:, Uniform tilings of 3-space.
17550:
17541:
17526:
17517:
17462:, and two tetrahedra from the
15266:
15228:
14982:
14797:Omnitruncated cubic honeycomb
14690:
14629:runcitruncated cubic honeycomb
14514:runcitruncated cubic honeycomb
14363:runcitruncated cubic honeycomb
14287:
14102:Runcitruncated cubic honeycomb
13574:snub rectified cubic honeycomb
13143:
13081:cantitruncated cubic honeycomb
12881:
12841:
12817:Omnitruncated alternate cubic
12714:cantitruncated cubic honeycomb
12625:cantitruncated cubic honeycomb
12549:
12303:Cantitruncated cubic honeycomb
12004:
11964:
11940:Bicantellated alternate cubic
11676:
11014:
10200:
10132:
10036:
9940:
9842:
9718:
9579:, which combine together as a
9539:list, with its dual called an
9400:
8950:
8912:
8885:Bicantellated alternate cubic
8663:
7863:
7824:
7785:
7746:
7496:
7003:
6965:
6883:
6845:
6708:
6667:
6506:
6315:
6274:
6149:
6004:
1675:, Schläfli symbol {4,3,5}, of
1558:
223:
1:
17510:
15812:and has symmetry ]. It makes
15184:
15106:omnitruncated cubic honeycomb
15038:omnitruncated cubic honeycomb
14790:Omnitruncated cubic honeycomb
14406:Its name is derived from its
12792:
11912:
11817:It is closely related to the
11736:cantellated cubic cellulation
9823:
9687:
9505:. Being composed entirely of
8863:
1656:It is related to the regular
378:hyperbolic uniform honeycombs
361:in any number of dimensions.
17609:Uniform Panoploid Tetracombs
17446:and has symmetry . It makes
16370:Biorthosnub cubic honeycomb
16011:
15409:
15325:
14740:(as triangular antiprisms),
14060:(as triangular antiprisms),
13674:
13054:
12939:
12807:
12651:in a ratio of 1:1:3, with a
12164:
12124:
11927:
11800:
11758:in a ratio of 1:1:3, with a
11445:Cantellated cubic honeycomb
11411:
11269:
10525:
10483:
10389:
9200:Bitruncated cubic honeycomb
9129:
9016:
8997:
8878:
8252:
8217:
8128:
7963:
7930:
7723:
1455:
1394:
1324:
1214:
1172:
1106:
1015:
872:
667:
627:
589:
549:
467:
7:
17642:(Paper 22) H.S.M. Coxeter,
17557:cantic snub cubic honeycomb
17472:
16600:symmetry) and two kinds of
16546:biorthosnub cubic honeycomb
16363:Biorthosnub cubic honeycomb
15932:pentagonal icositetrahedron
15044:is a uniform space-filling
13956:cantic snub cubic honeycomb
13771:Cantic snub cubic honeycomb
12690:
12631:is a uniform space-filling
12240:quarter oblate octahedrille
12236:cantellated cubic honeycomb
12230:Quarter oblate octahedrille
12201:. Other variants result in
11834:cantellated cubic honeycomb
11777:quarter oblate octahedrille
11738:is a uniform space-filling
11732:cantellated cubic honeycomb
11706:quarter oblate octahedrille
11438:Cantellated cubic honeycomb
11181:α-rhombohedral crystal
10647:symmetry and consists of 2
9569:bitruncated cubic honeycomb
9472:bitruncated cubic honeycomb
9193:Bitruncated cubic honeycomb
8726:is a uniform space-filling
8724:truncated cubic cellulation
8398:elongated square bipyramids
7700:
7563:is a uniform space-filling
7561:rectified cubic cellulation
3970:{p,3,p} regular honeycombs
2927:{4,3,p} regular honeycombs
1695:{p,3,4} regular honeycombs
835:There is a large number of
10:
18604:
17484:Alternated cubic honeycomb
15060:in a ratio of 1:3, with a
14761:augmented triangular prism
14633:square quarter pyramidille
14623:Square quarter pyramidille
14468:square quarter pyramidille
14371:space-filling tessellation
14337:square quarter pyramidille
13962:in a way that leaves only
13778:Orthosnub cubic honeycomb
12820:
11943:
11937:Truncated cubic honeycomb
11802:
9822:
8891:
8888:Truncated cubic honeycomb
8423:Truncated cubic honeycomb
8396:. The dual is composed of
7725:
7579:in a ratio of 1:1, with a
7065:Rectified cubic honeycomb
3969:
2926:
1694:
17678:
17489:List of regular polytopes
17160:convex uniform honeycombs
17151:It is constructed from a
16890:convex uniform honeycombs
16881:It is constructed from a
15125:
14593:Related skew apeirohedron
14533:
14452:from its relation to the
12733:
12191:rectified cubic honeycomb
11853:
11796:
11044:Ten-of-diamonds honeycomb
9600:
9573:rhombitrihexagonal tiling
9498:around each vertex, in a
8804:
8785:truncated cubic honeycomb
8720:truncated cubic honeycomb
8416:Truncated cubic honeycomb
7971:
7964:
7641:
7622:rectified cubic honeycomb
7557:rectified cubic honeycomb
7058:Rectified cubic honeycomb
6792:
6779:
6038:
5986:This honeycomb is one of
5295:
4379:
4007:
3985:
2966:
2944:
1734:
1712:
1592:
417:convex uniform polyhedral
370:convex uniform honeycombs
368:("flat") space, like the
18072:Uniform convex honeycomb
17575:The Symmetries of Things
15936:tetragonal trapezohedron
15764:omnisnub cubic honeycomb
14755:-symmetric wedges), and
14071:-symmetric wedges), and
13247:-symmetric wedges), and
384:can be projected to its
328:called this honeycomb a
17494:Order-5 cubic honeycomb
16883:truncated square tiling
15193:form has two colors of
15112:Orthogonal projections
15073:calls this honeycomb a
14520:Orthogonal projections
14462:calls this honeycomb a
12803:truncated cuboctahedron
12720:Orthogonal projections
12664:calls this honeycomb a
11840:Orthogonal projections
11771:calls this honeycomb a
11187:Five uniform colorings
10630:pyritohedral icosahedra
9587:Orthogonal projections
9581:chamfered square tiling
9577:truncated square tiling
9531:calls this honeycomb a
8791:Orthogonal projections
8755:calls this honeycomb a
7628:Orthogonal projections
7592:calls this honeycomb a
6031:Coxeter–Dynkin diagrams
1673:order-5 cubic honeycomb
1579:Orthogonal projections
18006:
17964:
17928:
17891:
17848:
17805:
17762:
17390:can be constructed by
17210:Coxeter-Dynkin diagram
17155:extruded into prisms.
16932:Coxeter-Dynkin diagram
16885:extruded into prisms.
16663:Coxeter-Dynkin diagram
15818:truncated cuboctahedra
15766:can be constructed by
15496:truncated cuboctahedra
15282:
15244:
15205:Two uniform colorings
15195:truncated cuboctahedra
15054:truncated cuboctahedra
14998:
14706:
14303:
13159:
13085:triangular pyramidille
13075:Triangular pyramidille
12897:
12857:
12670:triangular pyramidille
12641:truncated cuboctahedra
12599:triangular pyramidille
12565:
12244:catoptric tessellation
12020:
11980:
11692:
11075:bisnub cubic honeycomb
11030:
10216:
10148:
10052:
9956:
9858:
9734:
9694:disphenoid tetrahedron
9553:disphenoid tetrahedron
9533:truncated octahedrille
9467:
9416:
9247:Coxeter-Dynkin diagram
8966:
8928:
8679:
7879:
7840:
7801:
7762:
7512:
7019:
6981:
6899:
6861:
6724:
6683:
6522:
6331:
6290:
6165:
6020:
408:, {4,4} in the plane.
347:or higher-dimensional
239:
18588:Regular tessellations
18446:Uniform 10-honeycomb
18007:
17965:
17929:
17892:
17849:
17806:
17763:
17571:Chaim Goodman-Strauss
17464:triangular bipyramids
17133:. It is composed of
16863:. It is composed of
15832:cells from the gaps.
15283:
15245:
14999:
14707:
14601:exists with the same
14395:isosceles-trapezoidal
14304:
14259:isosceles-trapezoidal
13160:
12898:
12858:
12814:Cantitruncated cubic
12566:
12021:
11981:
11693:
11031:
10217:
10149:
10053:
9957:
9859:
9749:Wythoff constructions
9735:
9696:, and it is also the
9547:. Although a regular
9500:tetragonal disphenoid
9465:
9417:
9348:tetragonal disphenoid
8967:
8929:
8680:
7880:
7841:
7802:
7763:
7513:
7020:
6982:
6900:
6862:
6725:
6684:
6523:
6332:
6291:
6166:
6021:
240:
18573:Regular 3-honeycombs
17974:
17938:
17902:
17859:
17816:
17773:
17730:
17611:, Manuscript (2006)
16502:Tetragonal antiwedge
15519:triangular bipyramid
15442:exist with the same
15438:Two related uniform
15256:
15218:
14972:
14680:
14597:Two related uniform
14450:Wythoff construction
14277:
13236:(as square prisms),
13191:vertex configuration
13133:
12871:
12831:
12539:
11994:
11954:
11819:perovskite structure
11666:
11004:
10623:triangular bipyramid
10190:
10122:
10026:
9930:
9832:
9708:
9541:oblate tetrahedrille
9494:cubes). It has four
9430:Oblate tetrahedrille
9390:
8940:
8902:
8653:
7853:
7814:
7775:
7736:
7715:Wythoff construction
7486:
6993:
6955:
6873:
6835:
6698:
6657:
6496:
6305:
6264:
6139:
5994:
2914:and honeycombs with
2910:It in a sequence of
398:hypercube honeycombs
374:non-Euclidean spaces
213:
18578:Regular 4-polytopes
18406:Uniform 9-honeycomb
18339:Uniform 8-honeycomb
18277:Uniform 7-honeycomb
18222:Uniform 6-honeycomb
18173:Uniform 5-honeycomb
18121:Uniform 4-honeycomb
17705:Fundamental convex
17662:Klitzing, Richard.
17141:in a ratio of 1:2.
17121:is a space-filling
16871:in a ratio of 1:1.
16851:is a space-filling
16009:
15990:octahedral symmetry
15206:
15113:
14521:
13960:truncated octahedra
13226:truncated octahedra
13198:
13185:It is related to a
12805:cells alternating.
12721:
12645:truncated octahedra
11930:
11841:
11188:
10657:isosceles triangles
10608:truncated octahedra
10392:truncated octahedra
9756:
9698:Goursat tetrahedron
9588:
9507:truncated octahedra
9496:truncated octahedra
9490:(or, equivalently,
9488:truncated octahedra
9474:is a space-filling
8792:
8322:scaliform honeycomb
8310:trihexagonal tiling
7629:
7598:oblate octahedrille
7527:oblate octahedrille
6080:Honeycomb diagrams
5990:constructed by the
4048:{∞,3,∞}
1580:
337:geometric honeycomb
55:Hypercube honeycomb
18002:
17960:
17924:
17887:
17844:
17801:
17758:
17711:uniform honeycombs
17607:George Olshevsky,
17153:snub square tiling
16591:rhombicuboctahedra
16319:rhombicuboctahedra
16007:
15828:, and creates new
15444:vertex arrangement
15278:
15240:
15204:
15111:
15079:eighth pyramidille
15071:John Horton Conway
15062:phyllic disphenoid
15012:eighth pyramidille
14994:
14940:Fibrifold notation
14929:phyllic disphenoid
14734:rhombicuboctahedra
14702:
14603:vertex arrangement
14599:skew apeirohedrons
14519:
14460:John Horton Conway
14379:rhombicuboctahedra
14318:Fibrifold notation
14299:
14013:rhombicuboctahedra
13196:
13155:
12893:
12853:
12719:
12662:John Horton Conway
12580:Fibrifold notation
12561:
12016:
11976:
11928:
11917:There is a second
11839:
11769:John Horton Conway
11748:rhombicuboctahedra
11688:
11642:Fibrifold notation
11186:
11026:
10212:
10144:
10048:
9952:
9854:
9754:
9730:
9702:fundamental domain
9586:
9557:isosceles triangle
9529:John Horton Conway
9523:uniform honeycombs
9521:. It is one of 28
9468:
9456:, cell-transitive
9412:
9359:Fibrifold notation
9329:isosceles triangle
8962:
8924:
8868:There is a second
8790:
8753:John Horton Conway
8675:
8630:Fibrifold notation
8318:triangular cupolae
8312:planes, using the
7875:
7836:
7797:
7758:
7627:
7596:, and its dual an
7590:John Horton Conway
7508:
7463:Fibrifold notation
7015:
6977:
6895:
6857:
6720:
6679:
6518:
6327:
6286:
6161:
6016:
1578:
869:Colors by letters
595:Rotation subgroup
511:Rotation subgroup
413:uniform honeycombs
392:Related honeycombs
326:John Horton Conway
320:tessellation with
235:
190:Fibrifold notation
18583:Self-dual tilings
18561:
18560:
18163:24-cell honeycomb
17987:
17951:
17915:
17872:
17829:
17786:
17743:
17713:in dimensions 2–9
17636:978-0-471-01003-6
17624:4(1994), 49 - 56.
17593:Regular Polytopes
17583:978-1-56881-220-5
17569:, Heidi Burgiel,
17448:square antiprisms
17384:
17383:
17378:Vertex-transitive
17139:triangular prisms
17131:Euclidean 3-space
17111:
17110:
17106:Vertex-transitive
16913:Uniform honeycomb
16861:Euclidean 3-space
16841:
16840:
16836:Vertex-transitive
16636:Uniform honeycomb
16542:
16541:
16536:Vertex-transitive
16349:triangular prisms
16266:
16265:
16260:Vertex-transitive
16074:
16073:
15975:
15974:
15822:square antiprisms
15756:
15755:
15750:Vertex-transitive
15552:square antiprisms
15490:Related polytopes
15487:
15486:
15440:skew apeirohedron
15434:Related polyhedra
15431:
15430:
15269:
15231:
15182:
15181:
15034:
15033:
15029:Vertex-transitive
14985:
14806:Uniform honeycomb
14746:triangular prisms
14728:Related polytopes
14693:
14590:
14589:
14505:
14504:
14456:cubic honeycomb.
14359:
14358:
14354:Vertex-transitive
14290:
14118:Uniform honeycomb
14062:triangular prisms
14048:Related polytopes
14035:triangular prisms
13952:
13951:
13946:Vertex-transitive
13767:
13766:
13566:
13565:
13560:Vertex-transitive
13238:triangular prisms
13220:Related polytopes
13217:
13216:
13187:skew apeirohedron
13146:
13072:
13071:
12884:
12844:
12790:
12789:
12653:mirrored sphenoid
12621:
12620:
12616:Vertex-transitive
12552:
12524:mirrored sphenoid
12319:Uniform honeycomb
12207:square antiprisms
12185:Related polytopes
12182:
12181:
12007:
11967:
11919:uniform colorings
11910:
11909:
11825:
11824:
11728:
11727:
11723:Vertex-transitive
11679:
11454:Uniform honeycomb
11434:
11433:
11067:
11066:
11061:Vertex-transitive
11017:
10661:scalene triangles
10602:Related polytopes
10599:
10598:
10203:
10135:
10039:
9943:
9845:
9721:
9685:
9684:
9519:vertex-transitive
9484:Euclidean 3-space
9460:
9459:
9450:Vertex-transitive
9403:
9224:Uniform honeycomb
9154:Related polytopes
9151:
9150:
8953:
8915:
8861:
8860:
8757:truncated cubille
8716:
8715:
8711:Vertex-transitive
8666:
8432:Uniform honeycomb
8384:Related polytopes
8306:
8305:
7866:
7827:
7788:
7749:
7707:uniform colorings
7698:
7697:
7553:
7552:
7544:Vertex-transitive
7499:
7074:Uniform honeycomb
7054:
7053:
7006:
6968:
6886:
6848:
6711:
6670:
6509:
6318:
6277:
6152:
6007:
5984:
5983:
5256:
5255:
4276:Related polytopes
4273:
4272:
3965:
3964:
2912:regular polytopes
2908:
2907:
1649:
1648:
1569:triangular tiling
1556:
1555:
1311:{4,4}×t{∞}
837:uniform colorings
831:Uniform colorings
828:
827:
302:Euclidean 3-space
290:cubic cellulation
282:
281:
273:Vertex-transitive
226:
45:Regular honeycomb
18595:
18011:
18009:
18008:
18003:
18001:
18000:
17989:
17988:
17980:
17969:
17967:
17966:
17961:
17959:
17958:
17953:
17952:
17944:
17933:
17931:
17930:
17925:
17923:
17922:
17917:
17916:
17908:
17896:
17894:
17893:
17888:
17886:
17885:
17874:
17873:
17865:
17853:
17851:
17850:
17845:
17843:
17842:
17831:
17830:
17822:
17810:
17808:
17807:
17802:
17800:
17799:
17788:
17787:
17779:
17767:
17765:
17764:
17759:
17757:
17756:
17745:
17744:
17736:
17699:
17692:
17685:
17676:
17675:
17667:
17559:
17554:
17548:
17545:
17539:
17530:
17524:
17521:
17452:octagonal prisms
17445:
17444:
17443:
17439:
17438:
17434:
17433:
17429:
17428:
17424:
17423:
17419:
17418:
17414:
17413:
17409:
17408:
17404:
17403:
17360:
17332:
17323:
17308:
17307:
17306:
17302:
17301:
17297:
17296:
17292:
17291:
17287:
17286:
17282:
17281:
17277:
17276:
17272:
17271:
17267:
17266:
17260:
17259:
17258:
17254:
17253:
17249:
17248:
17244:
17243:
17239:
17238:
17234:
17233:
17229:
17228:
17224:
17223:
17219:
17218:
17183:Convex honeycomb
17171:
17158:It is one of 28
17148:
17097:
17054:
17045:
17030:
17029:
17028:
17024:
17023:
17019:
17018:
17014:
17013:
17009:
17008:
17004:
17003:
16999:
16998:
16994:
16993:
16989:
16988:
16982:
16981:
16980:
16976:
16975:
16971:
16970:
16966:
16965:
16961:
16960:
16956:
16955:
16951:
16950:
16946:
16945:
16941:
16940:
16901:
16888:It is one of 28
16878:
16865:octagonal prisms
16827:
16785:
16776:
16761:
16760:
16759:
16755:
16754:
16750:
16749:
16745:
16744:
16740:
16739:
16735:
16734:
16730:
16729:
16725:
16724:
16720:
16719:
16713:
16712:
16711:
16707:
16706:
16702:
16701:
16697:
16696:
16692:
16691:
16687:
16686:
16682:
16681:
16677:
16676:
16672:
16671:
16653:tr{4,4}×{∞} or t
16624:
16588:
16587:
16586:
16582:
16581:
16577:
16576:
16572:
16571:
16567:
16566:
16562:
16561:
16557:
16556:
16527:
16498:
16468:
16459:
16440:
16439:
16438:
16434:
16433:
16429:
16428:
16424:
16423:
16419:
16418:
16414:
16413:
16409:
16408:
16400:Coxeter diagrams
16379:Convex honeycomb
16367:
16316:
16315:
16314:
16310:
16309:
16305:
16304:
16300:
16299:
16295:
16294:
16290:
16289:
16285:
16284:
16251:
16229:
16201:
16192:
16183:
16174:
16155:
16154:
16153:
16149:
16148:
16144:
16143:
16139:
16138:
16134:
16133:
16129:
16128:
16124:
16123:
16115:Coxeter diagrams
16094:Convex honeycomb
16082:
16070:
16063:
16056:
16049:
16040:
16033:
16026:
16017:
16010:
16006:
16000:
15923:
15911:
15910:
15909:
15905:
15904:
15900:
15899:
15895:
15894:
15890:
15889:
15885:
15884:
15880:
15879:
15840:
15826:octagonal prisms
15811:
15810:
15809:
15805:
15804:
15800:
15799:
15795:
15794:
15790:
15789:
15785:
15784:
15780:
15779:
15721:
15716:
15688:
15679:
15670:
15655:
15654:
15653:
15649:
15648:
15644:
15643:
15639:
15638:
15634:
15633:
15629:
15628:
15624:
15623:
15594:Convex honeycomb
15582:
15569:
15539:
15528:
15504:hexagonal prisms
15500:octagonal prisms
15483:
15476:
15467:
15458:
15449:
15448:
15427:
15420:
15406:
15405:
15404:
15400:
15399:
15395:
15394:
15387:
15386:
15385:
15381:
15380:
15376:
15375:
15371:
15370:
15366:
15365:
15361:
15360:
15356:
15355:
15341:
15334:
15308:
15301:
15287:
15285:
15284:
15279:
15277:
15276:
15271:
15270:
15262:
15249:
15247:
15246:
15241:
15239:
15238:
15233:
15232:
15224:
15207:
15203:
15199:octagonal prisms
15178:
15171:
15164:
15152:
15145:
15138:
15114:
15110:
15095:
15089:
15058:octagonal prisms
15020:
15003:
15001:
15000:
14995:
14993:
14992:
14987:
14986:
14978:
14952:
14944:Coxeter notation
14926:
14891:
14882:
14867:
14866:
14865:
14861:
14860:
14856:
14855:
14851:
14850:
14846:
14845:
14841:
14840:
14836:
14835:
14794:
14781:
14770:
14723:
14711:
14709:
14708:
14703:
14701:
14700:
14695:
14694:
14686:
14675:
14674:
14673:
14669:
14668:
14664:
14663:
14659:
14658:
14654:
14653:
14649:
14648:
14644:
14643:
14627:The dual to the
14618:
14613:
14586:
14579:
14572:
14560:
14553:
14546:
14522:
14518:
14501:
14494:
14487:
14480:
14473:
14472:
14447:
14446:
14445:
14441:
14440:
14436:
14435:
14431:
14430:
14426:
14425:
14421:
14420:
14416:
14415:
14387:octagonal prisms
14345:
14325:
14308:
14306:
14305:
14300:
14298:
14297:
14292:
14291:
14283:
14256:
14221:
14212:
14203:
14194:
14179:
14178:
14177:
14173:
14172:
14168:
14167:
14163:
14162:
14158:
14157:
14153:
14152:
14148:
14147:
14139:Coxeter diagrams
14106:
14093:
14082:
14010:
14009:
14008:
14004:
14003:
13999:
13998:
13994:
13993:
13989:
13988:
13984:
13983:
13979:
13978:
13937:
13915:
13885:
13876:
13867:
13848:
13847:
13846:
13842:
13841:
13837:
13836:
13832:
13831:
13827:
13826:
13822:
13821:
13817:
13816:
13808:Coxeter diagrams
13787:Convex honeycomb
13775:
13763:
13762:
13761:
13757:
13756:
13752:
13751:
13747:
13746:
13742:
13741:
13737:
13736:
13732:
13731:
13725:
13718:
13717:
13716:
13712:
13711:
13707:
13706:
13702:
13701:
13697:
13696:
13692:
13691:
13687:
13686:
13680:
13673:
13672:
13665:
13664:
13663:
13659:
13658:
13654:
13653:
13649:
13648:
13644:
13643:
13639:
13638:
13634:
13633:
13627:
13626:
13625:
13621:
13620:
13616:
13615:
13611:
13610:
13606:
13605:
13599:Coxeter diagrams
13551:
13544:
13543:
13542:
13538:
13537:
13533:
13532:
13528:
13527:
13523:
13522:
13518:
13517:
13513:
13512:
13491:
13486:
13456:
13447:
13438:
13423:
13422:
13421:
13417:
13416:
13412:
13411:
13407:
13406:
13402:
13401:
13397:
13396:
13392:
13391:
13385:
13384:
13383:
13379:
13378:
13374:
13373:
13369:
13368:
13364:
13363:
13357:
13356:
13355:
13351:
13350:
13346:
13345:
13341:
13340:
13336:
13335:
13331:
13330:
13326:
13325:
13317:Coxeter diagrams
13298:Convex honeycomb
13286:
13273:
13262:
13230:hexagonal prisms
13213:
13206:
13199:
13195:
13176:
13164:
13162:
13161:
13156:
13154:
13153:
13148:
13147:
13139:
13128:
13127:
13126:
13122:
13121:
13117:
13116:
13112:
13111:
13107:
13106:
13102:
13101:
13097:
13096:
13079:The dual of the
13051:
13044:
13030:
13029:
13028:
13024:
13023:
13019:
13018:
13014:
13013:
13009:
13008:
13001:
13000:
12999:
12995:
12994:
12990:
12989:
12985:
12984:
12980:
12979:
12975:
12974:
12970:
12969:
12955:
12948:
12922:
12915:
12902:
12900:
12899:
12894:
12892:
12891:
12886:
12885:
12877:
12862:
12860:
12859:
12854:
12852:
12851:
12846:
12845:
12837:
12808:
12786:
12779:
12772:
12760:
12753:
12746:
12722:
12718:
12703:
12686:
12680:
12607:
12587:
12570:
12568:
12567:
12562:
12560:
12559:
12554:
12553:
12545:
12521:
12516:
12481:
12472:
12463:
12448:
12447:
12446:
12442:
12441:
12437:
12436:
12432:
12431:
12427:
12426:
12422:
12421:
12417:
12416:
12410:
12409:
12408:
12404:
12403:
12399:
12398:
12394:
12393:
12389:
12388:
12382:
12381:
12380:
12376:
12375:
12371:
12370:
12366:
12365:
12361:
12360:
12356:
12355:
12351:
12350:
12307:
12298:
12286:
12285:
12284:
12280:
12279:
12275:
12274:
12270:
12269:
12265:
12264:
12260:
12259:
12255:
12254:
12234:The dual of the
12223:triangular prism
12161:
12154:
12140:
12133:
12121:
12120:
12119:
12115:
12114:
12110:
12109:
12105:
12104:
12100:
12099:
12092:
12091:
12090:
12086:
12085:
12081:
12080:
12076:
12075:
12071:
12070:
12066:
12065:
12061:
12060:
12045:
12038:
12025:
12023:
12022:
12017:
12015:
12014:
12009:
12008:
12000:
11985:
11983:
11982:
11977:
11975:
11974:
11969:
11968:
11960:
11931:
11906:
11899:
11892:
11880:
11873:
11866:
11842:
11838:
11815:
11808:
11801:
11792:
11787:
11714:
11697:
11695:
11694:
11689:
11687:
11686:
11681:
11680:
11672:
11649:
11628:
11616:
11607:
11598:
11583:
11582:
11581:
11577:
11576:
11572:
11571:
11567:
11566:
11562:
11561:
11557:
11556:
11552:
11551:
11545:
11544:
11543:
11539:
11538:
11534:
11533:
11529:
11528:
11524:
11523:
11517:
11516:
11515:
11511:
11510:
11506:
11505:
11501:
11500:
11496:
11495:
11491:
11490:
11486:
11485:
11442:
11408:
11407:
11406:
11402:
11401:
11397:
11396:
11392:
11391:
11387:
11386:
11379:
11378:
11377:
11373:
11372:
11368:
11367:
11360:
11359:
11358:
11354:
11353:
11349:
11348:
11344:
11343:
11339:
11338:
11331:
11330:
11329:
11325:
11324:
11320:
11319:
11315:
11314:
11310:
11309:
11305:
11304:
11300:
11299:
11292:
11291:
11290:
11286:
11285:
11281:
11280:
11221:
11214:
11207:
11200:
11189:
11185:
11175:
11174:
11173:
11169:
11168:
11164:
11163:
11159:
11158:
11154:
11153:
11147:
11146:
11145:
11141:
11140:
11136:
11135:
11131:
11130:
11126:
11125:
11119:
11118:
11117:
11113:
11112:
11108:
11107:
11103:
11102:
11098:
11097:
11093:
11092:
11088:
11087:
11080:Coxeter diagrams
11052:
11035:
11033:
11032:
11027:
11025:
11024:
11019:
11018:
11010:
10990:
10967:
10958:
10943:
10942:
10941:
10937:
10936:
10932:
10931:
10927:
10926:
10922:
10921:
10917:
10916:
10912:
10911:
10905:
10904:
10903:
10899:
10898:
10894:
10893:
10889:
10888:
10884:
10883:
10877:
10876:
10875:
10871:
10870:
10866:
10865:
10861:
10860:
10856:
10855:
10851:
10850:
10846:
10845:
10839:
10838:
10837:
10833:
10832:
10828:
10827:
10823:
10822:
10818:
10817:
10811:
10810:
10809:
10805:
10804:
10800:
10799:
10795:
10794:
10790:
10789:
10785:
10784:
10780:
10779:
10773:
10772:
10771:
10767:
10766:
10762:
10761:
10757:
10756:
10752:
10751:
10745:
10744:
10743:
10739:
10738:
10734:
10733:
10729:
10728:
10724:
10723:
10719:
10718:
10714:
10713:
10705:Coxeter diagrams
10684:Convex honeycomb
10672:
10612:hexagonal prisms
10595:
10588:
10581:
10574:
10567:
10522:
10515:
10508:
10501:
10494:
10480:
10474:
10465:
10459:
10453:
10447:
10438:
10432:
10426:
10417:
10411:
10402:
10386:
10385:
10384:
10380:
10379:
10375:
10374:
10367:
10366:
10365:
10361:
10360:
10356:
10355:
10351:
10350:
10346:
10345:
10338:
10337:
10336:
10332:
10331:
10327:
10326:
10322:
10321:
10317:
10316:
10309:
10308:
10307:
10303:
10302:
10298:
10297:
10293:
10292:
10288:
10287:
10283:
10282:
10278:
10277:
10270:
10269:
10268:
10264:
10263:
10259:
10258:
10244:
10243:
10242:
10238:
10237:
10233:
10232:
10221:
10219:
10218:
10213:
10211:
10210:
10205:
10204:
10196:
10184:
10183:
10182:
10178:
10177:
10173:
10172:
10168:
10167:
10163:
10162:
10153:
10151:
10150:
10145:
10143:
10142:
10137:
10136:
10128:
10116:
10115:
10114:
10110:
10109:
10105:
10104:
10100:
10099:
10095:
10094:
10088:
10087:
10086:
10082:
10081:
10077:
10076:
10072:
10071:
10067:
10066:
10057:
10055:
10054:
10049:
10047:
10046:
10041:
10040:
10032:
10020:
10019:
10018:
10014:
10013:
10009:
10008:
10002:
10001:
10000:
9996:
9995:
9991:
9990:
9986:
9985:
9981:
9980:
9976:
9975:
9971:
9970:
9961:
9959:
9958:
9953:
9951:
9950:
9945:
9944:
9936:
9924:
9923:
9922:
9918:
9917:
9913:
9912:
9906:
9905:
9904:
9900:
9899:
9895:
9894:
9890:
9889:
9885:
9884:
9880:
9879:
9875:
9874:
9863:
9861:
9860:
9855:
9853:
9852:
9847:
9846:
9838:
9796:
9789:
9782:
9775:
9768:
9757:
9753:
9739:
9737:
9736:
9731:
9729:
9728:
9723:
9722:
9714:
9681:
9674:
9667:
9660:
9653:
9641:
9634:
9627:
9620:
9613:
9589:
9585:
9543:, also called a
9441:
9421:
9419:
9418:
9413:
9411:
9410:
9405:
9404:
9396:
9371:
9363:Coxeter notation
9345:
9302:
9287:
9286:
9285:
9281:
9280:
9276:
9275:
9271:
9270:
9266:
9265:
9261:
9260:
9256:
9255:
9215:
9209:
9197:
9184:
9173:
9147:
9140:
9126:
9125:
9124:
9120:
9119:
9115:
9114:
9110:
9109:
9105:
9104:
9100:
9099:
9095:
9094:
9087:
9086:
9085:
9081:
9080:
9076:
9075:
9071:
9070:
9066:
9065:
9061:
9060:
9056:
9055:
9049:
9048:
9047:
9043:
9042:
9038:
9037:
9033:
9032:
9028:
9027:
9013:
9006:
8993:
8986:
8971:
8969:
8968:
8963:
8961:
8960:
8955:
8954:
8946:
8933:
8931:
8930:
8925:
8923:
8922:
8917:
8916:
8908:
8879:
8870:uniform coloring
8857:
8850:
8843:
8831:
8824:
8817:
8793:
8789:
8775:
8770:
8702:
8684:
8682:
8681:
8676:
8674:
8673:
8668:
8667:
8659:
8637:
8615:
8585:
8576:
8561:
8560:
8559:
8555:
8554:
8550:
8549:
8545:
8544:
8540:
8539:
8535:
8534:
8530:
8529:
8523:
8522:
8521:
8517:
8516:
8512:
8511:
8507:
8506:
8502:
8501:
8495:
8494:
8493:
8489:
8488:
8484:
8483:
8479:
8478:
8474:
8473:
8469:
8468:
8464:
8463:
8455:Coxeter diagrams
8420:
8407:
8394:square bifrustum
8378:
8368:coxeter notation
8361:
8360:
8359:
8355:
8354:
8350:
8349:
8345:
8344:
8340:
8339:
8335:
8334:
8330:
8329:
8249:
8242:
8235:
8228:
8214:
8213:
8212:
8208:
8207:
8203:
8202:
8198:
8197:
8193:
8192:
8185:
8184:
8183:
8179:
8178:
8174:
8173:
8169:
8168:
8164:
8163:
8156:
8155:
8154:
8150:
8149:
8145:
8144:
8140:
8139:
8135:
8134:
8125:
8124:
8123:
8119:
8118:
8114:
8113:
8109:
8108:
8104:
8103:
8099:
8098:
8094:
8093:
8086:
8085:
8084:
8080:
8079:
8075:
8074:
8070:
8069:
8065:
8064:
8060:
8059:
8055:
8054:
8047:
8046:
8045:
8041:
8040:
8036:
8035:
8031:
8030:
8026:
8025:
8021:
8020:
8016:
8015:
8008:
8007:
8006:
8002:
8001:
7997:
7996:
7992:
7991:
7987:
7986:
7982:
7981:
7977:
7976:
7960:
7953:
7946:
7939:
7924:
7915:
7906:
7897:
7884:
7882:
7881:
7876:
7874:
7873:
7868:
7867:
7859:
7845:
7843:
7842:
7837:
7835:
7834:
7829:
7828:
7820:
7806:
7804:
7803:
7798:
7796:
7795:
7790:
7789:
7781:
7767:
7765:
7764:
7759:
7757:
7756:
7751:
7750:
7742:
7724:
7694:
7687:
7680:
7668:
7661:
7654:
7630:
7626:
7612:
7607:
7535:
7517:
7515:
7514:
7509:
7507:
7506:
7501:
7500:
7492:
7470:
7449:
7419:
7410:
7395:
7394:
7393:
7389:
7388:
7384:
7383:
7379:
7378:
7374:
7373:
7369:
7368:
7364:
7363:
7357:
7356:
7355:
7351:
7350:
7346:
7345:
7341:
7340:
7336:
7335:
7329:
7328:
7327:
7323:
7322:
7318:
7317:
7313:
7312:
7308:
7307:
7301:
7300:
7299:
7295:
7294:
7290:
7289:
7285:
7284:
7280:
7279:
7273:
7272:
7271:
7267:
7266:
7262:
7261:
7257:
7256:
7252:
7251:
7247:
7246:
7242:
7241:
7235:
7234:
7233:
7229:
7228:
7224:
7223:
7219:
7218:
7214:
7213:
7207:
7206:
7205:
7201:
7200:
7196:
7195:
7191:
7190:
7186:
7185:
7181:
7180:
7176:
7175:
7169:
7168:
7167:
7163:
7162:
7158:
7157:
7153:
7152:
7148:
7147:
7141:
7140:
7139:
7135:
7134:
7130:
7129:
7125:
7124:
7120:
7119:
7115:
7114:
7110:
7109:
7101:Coxeter diagrams
7062:
7044:
7043:
7042:
7038:
7037:
7033:
7032:
7024:
7022:
7021:
7016:
7014:
7013:
7008:
7007:
6999:
6986:
6984:
6983:
6978:
6976:
6975:
6970:
6969:
6961:
6938:
6924:
6923:
6922:
6918:
6917:
6913:
6912:
6904:
6902:
6901:
6896:
6894:
6893:
6888:
6887:
6879:
6866:
6864:
6863:
6858:
6856:
6855:
6850:
6849:
6841:
6828:
6827:
6826:
6822:
6821:
6817:
6816:
6809:
6808:
6807:
6803:
6802:
6798:
6797:
6785:
6772:
6758:
6757:
6756:
6752:
6751:
6747:
6746:
6742:
6741:
6737:
6736:
6729:
6727:
6726:
6721:
6719:
6718:
6713:
6712:
6704:
6688:
6686:
6685:
6680:
6678:
6677:
6672:
6671:
6663:
6651:
6650:
6649:
6645:
6644:
6640:
6639:
6635:
6634:
6630:
6629:
6625:
6624:
6620:
6619:
6612:
6611:
6610:
6606:
6605:
6601:
6600:
6596:
6595:
6591:
6590:
6578:
6564:
6550:
6549:
6548:
6544:
6543:
6539:
6538:
6527:
6525:
6524:
6519:
6517:
6516:
6511:
6510:
6502:
6490:
6489:
6488:
6484:
6483:
6479:
6478:
6474:
6473:
6469:
6468:
6464:
6463:
6459:
6458:
6451:
6450:
6449:
6445:
6444:
6440:
6439:
6427:
6413:
6399:
6398:
6397:
6393:
6392:
6388:
6387:
6383:
6382:
6378:
6377:
6365:
6364:
6363:
6359:
6358:
6354:
6353:
6349:
6348:
6344:
6343:
6336:
6334:
6333:
6328:
6326:
6325:
6320:
6319:
6311:
6295:
6293:
6292:
6287:
6285:
6284:
6279:
6278:
6270:
6258:
6257:
6256:
6252:
6251:
6247:
6246:
6242:
6241:
6237:
6236:
6229:
6228:
6227:
6223:
6222:
6218:
6217:
6213:
6212:
6208:
6207:
6195:
6181:
6170:
6168:
6167:
6162:
6160:
6159:
6154:
6153:
6145:
6133:
6132:
6131:
6127:
6126:
6122:
6121:
6117:
6116:
6112:
6111:
6102:
6088:
6036:
6035:
6025:
6023:
6022:
6017:
6015:
6014:
6009:
6008:
6000:
5974:
5973:
5972:
5968:
5967:
5963:
5962:
5958:
5957:
5953:
5952:
5941:
5940:
5939:
5935:
5934:
5930:
5929:
5925:
5924:
5920:
5919:
5908:
5907:
5906:
5902:
5901:
5897:
5896:
5892:
5891:
5887:
5886:
5875:
5874:
5873:
5869:
5868:
5864:
5863:
5859:
5858:
5854:
5853:
5842:
5841:
5840:
5836:
5835:
5831:
5830:
5826:
5825:
5821:
5820:
5809:
5808:
5807:
5803:
5802:
5798:
5797:
5793:
5792:
5788:
5787:
5776:
5775:
5774:
5770:
5769:
5765:
5764:
5760:
5759:
5755:
5754:
5743:
5742:
5741:
5737:
5736:
5732:
5731:
5727:
5726:
5722:
5721:
5705:
5692:
5691:
5690:
5686:
5685:
5681:
5680:
5676:
5675:
5671:
5670:
5659:
5658:
5657:
5653:
5652:
5648:
5647:
5643:
5642:
5638:
5637:
5627:
5626:
5625:
5621:
5620:
5616:
5615:
5611:
5610:
5606:
5605:
5598:
5597:
5596:
5592:
5591:
5587:
5586:
5582:
5581:
5577:
5576:
5558:
5545:
5544:
5543:
5539:
5538:
5534:
5533:
5529:
5528:
5524:
5523:
5512:
5511:
5510:
5506:
5505:
5501:
5500:
5496:
5495:
5491:
5490:
5479:
5478:
5477:
5473:
5472:
5468:
5467:
5463:
5462:
5458:
5457:
5446:
5445:
5444:
5440:
5439:
5435:
5434:
5430:
5429:
5425:
5424:
5414:
5413:
5412:
5408:
5407:
5403:
5402:
5398:
5397:
5393:
5392:
5388:
5387:
5383:
5382:
5375:
5374:
5373:
5369:
5368:
5364:
5363:
5359:
5358:
5354:
5353:
5336:
5293:
5292:
5285:
5284:
5283:
5279:
5278:
5274:
5273:
5269:
5268:
5264:
5263:
5246:
5245:
5244:
5240:
5239:
5235:
5234:
5223:
5222:
5221:
5217:
5216:
5212:
5211:
5200:
5199:
5198:
5194:
5193:
5189:
5188:
5177:
5176:
5175:
5171:
5170:
5166:
5165:
5149:
5135:
5134:
5133:
5129:
5128:
5124:
5123:
5113:
5112:
5111:
5107:
5106:
5102:
5101:
5094:
5093:
5092:
5088:
5087:
5083:
5082:
5064:
5050:
5049:
5048:
5044:
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5039:
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5028:
5027:
5026:
5022:
5021:
5017:
5016:
5000:
4987:
4986:
4985:
4981:
4980:
4976:
4975:
4971:
4970:
4966:
4965:
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4960:
4956:
4955:
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4942:
4938:
4937:
4933:
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4918:
4917:
4913:
4912:
4901:
4900:
4899:
4895:
4894:
4890:
4889:
4885:
4884:
4880:
4879:
4875:
4874:
4870:
4869:
4858:
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4856:
4852:
4851:
4847:
4846:
4842:
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4837:
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4832:
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4827:
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4814:
4810:
4809:
4805:
4804:
4800:
4799:
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4794:
4787:
4786:
4785:
4781:
4780:
4776:
4775:
4771:
4770:
4766:
4765:
4761:
4760:
4756:
4755:
4738:
4725:
4724:
4723:
4719:
4718:
4714:
4713:
4709:
4708:
4704:
4703:
4699:
4698:
4694:
4693:
4682:
4681:
4680:
4676:
4675:
4671:
4670:
4666:
4665:
4661:
4660:
4656:
4655:
4651:
4650:
4638:
4637:
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4632:
4631:
4627:
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4622:
4621:
4617:
4616:
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4611:
4607:
4606:
4595:
4594:
4593:
4589:
4588:
4584:
4583:
4579:
4578:
4574:
4573:
4569:
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4545:
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4535:
4531:
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4521:
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4509:
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4507:
4503:
4502:
4498:
4497:
4493:
4492:
4488:
4487:
4483:
4482:
4478:
4477:
4467:
4466:
4465:
4461:
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4456:
4455:
4451:
4450:
4446:
4445:
4441:
4440:
4436:
4435:
4420:
4377:
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4365:
4364:
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4339:
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4334:
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4232:
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3427:
3426:
3422:
3421:
3417:
3416:
3412:
3411:
3405:
3404:
3403:
3399:
3398:
3394:
3393:
3389:
3388:
3384:
3383:
3379:
3378:
3374:
3373:
3362:
3361:
3360:
3356:
3355:
3351:
3350:
3346:
3345:
3341:
3340:
3336:
3335:
3331:
3330:
3319:
3318:
3317:
3313:
3312:
3308:
3307:
3303:
3302:
3298:
3297:
3293:
3292:
3288:
3287:
3281:
3280:
3279:
3275:
3274:
3270:
3269:
3265:
3264:
3260:
3259:
3253:
3252:
3251:
3247:
3246:
3242:
3241:
3237:
3236:
3232:
3231:
3227:
3226:
3222:
3221:
3210:
3209:
3208:
3204:
3203:
3199:
3198:
3194:
3193:
3189:
3188:
3184:
3183:
3179:
3178:
3167:
3166:
3165:
3161:
3160:
3156:
3155:
3151:
3150:
3146:
3145:
3141:
3140:
3136:
3135:
3131:
3130:
3124:
3123:
3122:
3118:
3117:
3113:
3112:
3108:
3107:
3103:
3102:
3096:
3095:
3094:
3090:
3089:
3085:
3084:
3080:
3079:
3075:
3074:
3070:
3069:
3065:
3064:
3053:
3052:
3051:
3047:
3046:
3042:
3041:
3037:
3036:
3032:
3031:
3027:
3026:
3022:
3021:
3010:
3009:
3008:
3004:
3003:
2999:
2998:
2994:
2993:
2989:
2988:
2984:
2983:
2979:
2978:
2924:
2923:
2904:
2903:
2902:
2898:
2897:
2893:
2892:
2888:
2887:
2883:
2882:
2872:
2865:
2864:
2863:
2859:
2858:
2854:
2853:
2849:
2848:
2844:
2843:
2833:
2826:
2825:
2824:
2820:
2819:
2815:
2814:
2810:
2809:
2805:
2804:
2794:
2787:
2786:
2785:
2781:
2780:
2776:
2775:
2771:
2770:
2766:
2765:
2755:
2748:
2747:
2746:
2742:
2741:
2737:
2736:
2732:
2731:
2727:
2726:
2716:
2709:
2708:
2707:
2703:
2702:
2698:
2697:
2693:
2692:
2688:
2687:
2677:
2670:
2669:
2668:
2664:
2663:
2659:
2658:
2654:
2653:
2649:
2648:
2638:
2626:
2619:
2612:
2605:
2598:
2591:
2584:
2572:
2571:
2570:
2566:
2565:
2561:
2560:
2556:
2555:
2551:
2550:
2546:
2545:
2541:
2540:
2536:
2535:
2529:
2528:
2527:
2523:
2522:
2518:
2517:
2513:
2512:
2508:
2507:
2503:
2502:
2498:
2497:
2493:
2492:
2486:
2485:
2484:
2480:
2479:
2475:
2474:
2470:
2469:
2465:
2464:
2458:
2457:
2456:
2452:
2451:
2447:
2446:
2442:
2441:
2437:
2436:
2432:
2431:
2427:
2426:
2414:
2413:
2412:
2408:
2407:
2403:
2402:
2398:
2397:
2393:
2392:
2388:
2387:
2383:
2382:
2378:
2377:
2371:
2370:
2369:
2365:
2364:
2360:
2359:
2355:
2354:
2350:
2349:
2345:
2344:
2340:
2339:
2335:
2334:
2328:
2327:
2326:
2322:
2321:
2317:
2316:
2312:
2311:
2307:
2306:
2300:
2299:
2298:
2294:
2293:
2289:
2288:
2284:
2283:
2279:
2278:
2274:
2273:
2269:
2268:
2257:
2256:
2255:
2251:
2250:
2246:
2245:
2241:
2240:
2236:
2235:
2229:
2228:
2227:
2223:
2222:
2218:
2217:
2213:
2212:
2208:
2207:
2203:
2202:
2198:
2197:
2186:
2185:
2184:
2180:
2179:
2175:
2174:
2170:
2169:
2165:
2164:
2160:
2159:
2155:
2154:
2148:
2147:
2146:
2142:
2141:
2137:
2136:
2132:
2131:
2127:
2126:
2122:
2121:
2117:
2116:
2110:
2109:
2108:
2104:
2103:
2099:
2098:
2094:
2093:
2089:
2088:
2082:
2081:
2080:
2076:
2075:
2071:
2070:
2066:
2065:
2061:
2060:
2056:
2055:
2051:
2050:
2039:
2038:
2037:
2033:
2032:
2028:
2027:
2023:
2022:
2018:
2017:
2011:
2010:
2009:
2005:
2004:
2000:
1999:
1995:
1994:
1990:
1989:
1985:
1984:
1980:
1979:
1968:
1967:
1966:
1962:
1961:
1957:
1956:
1952:
1951:
1947:
1946:
1942:
1941:
1937:
1936:
1932:
1931:
1925:
1924:
1923:
1919:
1918:
1914:
1913:
1909:
1908:
1904:
1903:
1899:
1898:
1894:
1893:
1889:
1888:
1882:
1881:
1880:
1876:
1875:
1871:
1870:
1866:
1865:
1861:
1860:
1854:
1853:
1852:
1848:
1847:
1843:
1842:
1838:
1837:
1833:
1832:
1828:
1827:
1823:
1822:
1811:
1810:
1809:
1805:
1804:
1800:
1799:
1795:
1794:
1790:
1789:
1783:
1782:
1781:
1777:
1776:
1772:
1771:
1767:
1766:
1762:
1761:
1757:
1756:
1752:
1751:
1692:
1691:
1677:hyperbolic space
1645:
1638:
1631:
1619:
1612:
1605:
1581:
1577:
1549:
1539:
1538:
1537:
1533:
1532:
1528:
1527:
1523:
1522:
1518:
1517:
1513:
1512:
1508:
1507:
1501:
1500:
1499:
1495:
1494:
1490:
1489:
1485:
1484:
1480:
1479:
1475:
1474:
1470:
1469:
1465:
1464:
1449:
1439:
1438:
1437:
1433:
1432:
1428:
1427:
1423:
1422:
1418:
1417:
1413:
1412:
1408:
1407:
1403:
1402:
1388:
1381:{4,4}×{∞}
1374:
1373:
1372:
1368:
1367:
1363:
1362:
1358:
1357:
1353:
1352:
1348:
1347:
1343:
1342:
1338:
1337:
1333:
1332:
1318:
1308:
1307:
1306:
1302:
1301:
1297:
1296:
1292:
1291:
1287:
1286:
1282:
1281:
1277:
1276:
1272:
1271:
1264:
1263:
1262:
1258:
1257:
1253:
1252:
1248:
1247:
1243:
1242:
1238:
1237:
1233:
1232:
1228:
1227:
1223:
1222:
1199:
1198:
1197:
1193:
1192:
1188:
1187:
1179:
1166:
1152:
1151:
1150:
1146:
1145:
1141:
1140:
1136:
1135:
1131:
1130:
1126:
1125:
1121:
1120:
1112:
1100:
1090:
1089:
1088:
1084:
1083:
1079:
1078:
1074:
1073:
1069:
1068:
1064:
1063:
1059:
1058:
1052:
1051:
1050:
1046:
1045:
1041:
1040:
1036:
1035:
1031:
1030:
1022:
1009:
999:
998:
997:
993:
992:
988:
987:
983:
982:
978:
977:
973:
972:
968:
967:
961:
960:
959:
955:
954:
950:
949:
945:
944:
940:
939:
935:
934:
930:
929:
925:
924:
918:
917:
916:
912:
911:
907:
906:
902:
901:
897:
896:
892:
891:
887:
886:
878:
846:Coxeter notation
842:
841:
824:
823:
822:
818:
817:
813:
812:
808:
807:
803:
802:
798:
797:
793:
792:
782:
781:
780:
776:
775:
771:
770:
766:
765:
761:
760:
756:
755:
751:
750:
746:
745:
741:
740:
733:
732:
731:
727:
726:
722:
721:
717:
716:
712:
711:
707:
706:
702:
701:
697:
696:
692:
691:
687:
686:
682:
681:
630:Coxeter notation
621:
586:
579:
572:
565:
558:
430:
429:
411:It is one of 28
402:Schläfli symbols
382:uniform polytope
264:
244:
242:
241:
236:
234:
233:
228:
227:
219:
197:
176:
151:
136:
135:
134:
130:
129:
125:
124:
120:
119:
115:
114:
110:
109:
105:
104:
36:
31:
22:Cubic honeycomb
19:
18603:
18602:
18598:
18597:
18596:
18594:
18593:
18592:
18563:
18562:
18556:
18549:
18542:
18534:
18533:
18522:
18521:
18510:
18509:
18498:
18475:
18474:
18467:
18466:
18459:
18458:
18451:
18436:
18435:
18428:
18427:
18420:
18419:
18412:
18396:
18389:
18382:
18375:
18374:
18366:
18365:
18356:
18355:
18346:
18329:
18322:
18314:
18313:
18304:
18303:
18294:
18293:
18284:
18267:
18259:
18258:
18249:
18248:
18239:
18238:
18229:
18210:
18209:
18200:
18199:
18190:
18189:
18180:
18158:
18157:
18148:
18147:
18138:
18137:
18128:
18109:
18108:
18099:
18098:
18089:
18088:
18079:
18057:
18056:
18047:
18046:
18037:
18036:
18027:
17990:
17979:
17978:
17977:
17975:
17972:
17971:
17954:
17943:
17942:
17941:
17939:
17936:
17935:
17918:
17907:
17906:
17905:
17903:
17900:
17899:
17875:
17864:
17863:
17862:
17860:
17857:
17856:
17832:
17821:
17820:
17819:
17817:
17814:
17813:
17789:
17778:
17777:
17776:
17774:
17771:
17770:
17746:
17735:
17734:
17733:
17731:
17728:
17727:
17714:
17703:
17618:Branko Grünbaum
17589:Coxeter, H.S.M.
17563:
17562:
17555:
17551:
17546:
17542:
17531:
17527:
17522:
17518:
17513:
17500:Snub (geometry)
17475:
17469:
17441:
17436:
17431:
17426:
17421:
17416:
17411:
17406:
17401:
17399:
17396:Coxeter diagram
17344:
17324:
17304:
17299:
17294:
17289:
17284:
17279:
17274:
17269:
17264:
17262:
17261:
17256:
17251:
17246:
17241:
17236:
17231:
17226:
17221:
17216:
17214:
17203:
17199:
17197:
17190:Schläfli symbol
17169:
17164:
17091:
17080:
17066:
17046:
17026:
17021:
17016:
17011:
17006:
17001:
16996:
16991:
16986:
16984:
16983:
16978:
16973:
16968:
16963:
16958:
16953:
16948:
16943:
16938:
16936:
16925:
16920:Schläfli symbol
16899:
16894:
16821:
16797:
16777:
16757:
16752:
16747:
16742:
16737:
16732:
16727:
16722:
16717:
16715:
16714:
16709:
16704:
16699:
16694:
16689:
16684:
16679:
16674:
16669:
16667:
16656:
16652:
16650:
16647:t{4,4}×{∞} or t
16643:Schläfli symbol
16622:
16617:
16613:
16598:
16584:
16579:
16574:
16569:
16564:
16559:
16554:
16552:
16550:Coxeter diagram
16499:
16480:
16460:
16452:
16436:
16431:
16426:
16421:
16416:
16411:
16406:
16404:
16393:
16386:Schläfli symbol
16365:
16360:
16356:
16347:symmetry), and
16345:
16332:, two kinds of
16326:
16312:
16307:
16302:
16297:
16292:
16287:
16282:
16280:
16278:Coxeter diagram
16213:
16193:
16184:
16175:
16167:
16151:
16146:
16141:
16136:
16131:
16126:
16121:
16119:
16108:
16101:Schläfli symbol
16080:
16075:
16018:
15970:Cell-transitive
15938:
15934:
15907:
15902:
15897:
15892:
15887:
15882:
15877:
15875:
15871:Coxeter diagram
15864:
15857:Schläfli symbol
15838:
15807:
15802:
15797:
15792:
15787:
15782:
15777:
15775:
15772:Coxeter diagram
15700:
15680:
15671:
15651:
15646:
15641:
15636:
15631:
15626:
15621:
15619:
15615:Coxeter diagram
15608:
15601:Schläfli symbol
15580:
15575:
15570:
15540:
15529:
15515:
15492:
15462:
15453:
15436:
15402:
15397:
15392:
15390:
15383:
15378:
15373:
15368:
15363:
15358:
15353:
15351:
15347:Coxeter diagram
15306:
15299:
15272:
15261:
15260:
15259:
15257:
15254:
15253:
15234:
15223:
15222:
15221:
15219:
15216:
15215:
15191:Coxeter diagram
15187:
15102:
15077:, and its dual
15014:
14988:
14977:
14976:
14975:
14973:
14970:
14969:
14957:
14955:
14950:
14942:
14938:
14927:
14908:
14903:
14883:
14863:
14858:
14853:
14848:
14843:
14838:
14833:
14831:
14827:Coxeter diagram
14820:
14813:Schläfli symbol
14792:
14787:
14782:
14771:
14753:
14730:
14712:Coxeter group.
14696:
14685:
14684:
14683:
14681:
14678:
14677:
14671:
14666:
14661:
14656:
14651:
14646:
14641:
14639:
14637:Coxeter diagram
14625:
14595:
14510:
14466:, and its dual
14443:
14438:
14433:
14428:
14423:
14418:
14413:
14411:
14408:Coxeter diagram
14383:truncated cubes
14339:
14327:
14323:
14316:
14293:
14282:
14281:
14280:
14278:
14275:
14274:
14257:
14238:
14233:
14213:
14204:
14195:
14175:
14170:
14165:
14160:
14155:
14150:
14145:
14143:
14132:
14125:Schläfli symbol
14104:
14099:
14094:
14083:
14073:square pyramids
14069:
14050:
14042:
14033:symmetry), and
14031:
14020:
14006:
14001:
13996:
13991:
13986:
13981:
13976:
13974:
13972:Coxeter diagram
13897:
13877:
13868:
13860:
13844:
13839:
13834:
13829:
13824:
13819:
13814:
13812:
13801:
13794:Schläfli symbol
13773:
13768:
13759:
13754:
13749:
13744:
13739:
13734:
13729:
13727:
13726:
13714:
13709:
13704:
13699:
13694:
13689:
13684:
13682:
13681:
13661:
13656:
13651:
13646:
13641:
13636:
13631:
13629:
13623:
13618:
13613:
13608:
13603:
13601:
13596:
13589:
13545:
13540:
13535:
13530:
13525:
13520:
13515:
13510:
13508:
13468:
13448:
13439:
13419:
13414:
13409:
13404:
13399:
13394:
13389:
13387:
13381:
13376:
13371:
13366:
13361:
13359:
13358:
13353:
13348:
13343:
13338:
13333:
13328:
13323:
13321:
13310:
13305:Schläfli symbol
13284:
13279:
13274:
13263:
13245:
13222:
13183:
13149:
13138:
13137:
13136:
13134:
13131:
13130:
13124:
13119:
13114:
13109:
13104:
13099:
13094:
13092:
13089:Coxeter diagram
13077:
13067:
13063:
13059:
13057:
13026:
13021:
13016:
13011:
13006:
13004:
12997:
12992:
12987:
12982:
12977:
12972:
12967:
12965:
12961:Coxeter diagram
12920:
12913:
12887:
12876:
12875:
12874:
12872:
12869:
12868:
12863:
12847:
12836:
12835:
12834:
12832:
12829:
12828:
12799:Coxeter diagram
12795:
12710:
12693:
12668:, and its dual
12601:
12589:
12585:
12578:
12555:
12544:
12543:
12542:
12540:
12537:
12536:
12522:
12498:
12493:
12473:
12464:
12444:
12439:
12434:
12429:
12424:
12419:
12414:
12412:
12406:
12401:
12396:
12391:
12386:
12384:
12383:
12378:
12373:
12368:
12363:
12358:
12353:
12348:
12346:
12342:Coxeter diagram
12335:
12333:
12326:Schläfli symbol
12305:
12282:
12277:
12272:
12267:
12262:
12257:
12252:
12250:
12248:Coxeter diagram
12232:
12227:
12187:
12177:
12173:
12169:
12167:
12117:
12112:
12107:
12102:
12097:
12095:
12088:
12083:
12078:
12073:
12068:
12063:
12058:
12056:
12052:Coxeter diagram
12043:
12036:
12010:
11999:
11998:
11997:
11995:
11992:
11991:
11986:
11970:
11959:
11958:
11957:
11955:
11952:
11951:
11915:
11830:
11816:
11799:
11775:, and its dual
11708:
11682:
11671:
11670:
11669:
11667:
11664:
11663:
11651:
11647:
11640:
11629:
11608:
11599:
11579:
11574:
11569:
11564:
11559:
11554:
11549:
11547:
11541:
11536:
11531:
11526:
11521:
11519:
11518:
11513:
11508:
11503:
11498:
11493:
11488:
11483:
11481:
11477:Coxeter diagram
11470:
11468:
11461:Schläfli symbol
11440:
11435:
11426:
11404:
11399:
11394:
11389:
11384:
11382:
11375:
11370:
11365:
11363:
11356:
11351:
11346:
11341:
11336:
11334:
11327:
11322:
11317:
11312:
11307:
11302:
11297:
11295:
11288:
11283:
11278:
11276:
11272:Coxeter diagram
11219:
11212:
11205:
11198:
11171:
11166:
11161:
11156:
11151:
11149:
11143:
11138:
11133:
11128:
11123:
11121:
11115:
11110:
11105:
11100:
11095:
11090:
11085:
11083:
11046:
11020:
11009:
11008:
11007:
11005:
11002:
11001:
10959:
10939:
10934:
10929:
10924:
10919:
10914:
10909:
10907:
10901:
10896:
10891:
10886:
10881:
10879:
10878:
10873:
10868:
10863:
10858:
10853:
10848:
10843:
10841:
10835:
10830:
10825:
10820:
10815:
10813:
10812:
10807:
10802:
10797:
10792:
10787:
10782:
10777:
10775:
10769:
10764:
10759:
10754:
10749:
10747:
10746:
10741:
10736:
10731:
10726:
10721:
10716:
10711:
10709:
10698:
10696:
10691:Schläfli symbol
10670:
10665:
10645:
10619:
10604:
10559:
10557:
10550:
10546:
10542:
10538:
10534:
10530:
10528:
10469:
10442:
10421:
10406:
10397:
10382:
10377:
10372:
10370:
10363:
10358:
10353:
10348:
10343:
10341:
10334:
10329:
10324:
10319:
10314:
10312:
10305:
10300:
10295:
10290:
10285:
10280:
10275:
10273:
10266:
10261:
10256:
10254:
10250:Coxeter diagram
10240:
10235:
10230:
10228:
10227:
10225:
10223:
10206:
10195:
10194:
10193:
10191:
10188:
10187:
10180:
10175:
10170:
10165:
10160:
10158:
10157:
10155:
10154:
10138:
10127:
10126:
10125:
10123:
10120:
10119:
10112:
10107:
10102:
10097:
10092:
10090:
10084:
10079:
10074:
10069:
10064:
10062:
10061:
10059:
10058:
10042:
10031:
10030:
10029:
10027:
10024:
10023:
10016:
10011:
10006:
10004:
9998:
9993:
9988:
9983:
9978:
9973:
9968:
9966:
9965:
9963:
9962:
9946:
9935:
9934:
9933:
9931:
9928:
9927:
9920:
9915:
9910:
9908:
9902:
9897:
9892:
9887:
9882:
9877:
9872:
9870:
9869:
9867:
9865:
9848:
9837:
9836:
9835:
9833:
9830:
9829:
9794:
9787:
9780:
9773:
9766:
9724:
9713:
9712:
9711:
9709:
9706:
9705:
9690:
9565:
9515:edge-transitive
9511:cell-transitive
9454:edge-transitive
9435:
9431:
9406:
9395:
9394:
9393:
9391:
9388:
9387:
9376:
9374:
9369:
9361:
9357:
9346:
9314:
9283:
9278:
9273:
9268:
9263:
9258:
9253:
9251:
9240:
9236:
9231:Schläfli symbol
9195:
9190:
9185:
9174:
9156:
9122:
9117:
9112:
9107:
9102:
9097:
9092:
9090:
9083:
9078:
9073:
9068:
9063:
9058:
9053:
9051:
9045:
9040:
9035:
9030:
9025:
9023:
9019:Coxeter diagram
8991:
8984:
8972:
8956:
8945:
8944:
8943:
8941:
8938:
8937:
8918:
8907:
8906:
8905:
8903:
8900:
8899:
8866:
8781:
8759:, and its dual
8736:truncated cubes
8696:
8669:
8658:
8657:
8656:
8654:
8651:
8650:
8639:
8635:
8628:
8616:
8597:
8577:
8557:
8552:
8547:
8542:
8537:
8532:
8527:
8525:
8519:
8514:
8509:
8504:
8499:
8497:
8496:
8491:
8486:
8481:
8476:
8471:
8466:
8461:
8459:
8448:
8446:
8439:Schläfli symbol
8418:
8413:
8408:
8386:
8365:
8357:
8352:
8347:
8342:
8337:
8332:
8327:
8325:
8301:
8299:
8298:
8297:
8290:
8288:
8287:
8286:
8279:
8277:
8276:
8275:
8268:
8266:
8265:
8264:
8257:
8255:
8210:
8205:
8200:
8195:
8190:
8188:
8181:
8176:
8171:
8166:
8161:
8159:
8152:
8147:
8142:
8137:
8132:
8130:
8121:
8116:
8111:
8106:
8101:
8096:
8091:
8089:
8082:
8077:
8072:
8067:
8062:
8057:
8052:
8050:
8043:
8038:
8033:
8028:
8023:
8018:
8013:
8011:
8004:
7999:
7994:
7989:
7984:
7979:
7974:
7972:
7967:
7926:
7922:
7917:
7913:
7908:
7904:
7899:
7895:
7869:
7858:
7857:
7856:
7854:
7851:
7850:
7848:
7830:
7819:
7818:
7817:
7815:
7812:
7811:
7809:
7791:
7780:
7779:
7778:
7776:
7773:
7772:
7770:
7752:
7741:
7740:
7739:
7737:
7734:
7733:
7732:
7719:Coxeter diagram
7705:There are four
7703:
7618:
7594:cuboctahedrille
7548:edge-transitive
7529:
7502:
7491:
7490:
7489:
7487:
7484:
7483:
7472:
7468:
7461:
7450:
7431:
7411:
7391:
7386:
7381:
7376:
7371:
7366:
7361:
7359:
7353:
7348:
7343:
7338:
7333:
7331:
7325:
7320:
7315:
7310:
7305:
7303:
7297:
7292:
7287:
7282:
7277:
7275:
7274:
7269:
7264:
7259:
7254:
7249:
7244:
7239:
7237:
7231:
7226:
7221:
7216:
7211:
7209:
7208:
7203:
7198:
7193:
7188:
7183:
7178:
7173:
7171:
7165:
7160:
7155:
7150:
7145:
7143:
7142:
7137:
7132:
7127:
7122:
7117:
7112:
7107:
7105:
7094:
7092:
7090:
7088:
7081:Schläfli symbol
7060:
7055:
7050:
7040:
7035:
7030:
7028:
7009:
6998:
6997:
6996:
6994:
6991:
6990:
6988:
6971:
6960:
6959:
6958:
6956:
6953:
6952:
6948:
6940:
6936:
6930:
6920:
6915:
6910:
6908:
6889:
6878:
6877:
6876:
6874:
6871:
6870:
6868:
6851:
6840:
6839:
6838:
6836:
6833:
6832:
6824:
6819:
6814:
6812:
6810:
6805:
6800:
6795:
6793:
6789:
6773:
6770:
6764:
6754:
6749:
6744:
6739:
6734:
6732:
6714:
6703:
6702:
6701:
6699:
6696:
6695:
6693:
6692:
6673:
6662:
6661:
6660:
6658:
6655:
6654:
6647:
6642:
6637:
6632:
6627:
6622:
6617:
6615:
6613:
6608:
6603:
6598:
6593:
6588:
6586:
6582:
6566:
6562:
6556:
6546:
6541:
6536:
6534:
6531:
6512:
6501:
6500:
6499:
6497:
6494:
6493:
6486:
6481:
6476:
6471:
6466:
6461:
6456:
6454:
6452:
6447:
6442:
6437:
6435:
6431:
6415:
6411:
6405:
6395:
6390:
6385:
6380:
6375:
6373:
6371:
6361:
6356:
6351:
6346:
6341:
6339:
6321:
6310:
6309:
6308:
6306:
6303:
6302:
6300:
6299:
6280:
6269:
6268:
6267:
6265:
6262:
6261:
6254:
6249:
6244:
6239:
6234:
6232:
6230:
6225:
6220:
6215:
6210:
6205:
6203:
6199:
6183:
6179:
6155:
6144:
6143:
6142:
6140:
6137:
6136:
6129:
6124:
6119:
6114:
6109:
6107:
6090:
6086:
6076:
6071:
6065:
6058:
6046:
6010:
5999:
5998:
5997:
5995:
5992:
5991:
5978:
5970:
5965:
5960:
5955:
5950:
5948:
5945:
5937:
5932:
5927:
5922:
5917:
5915:
5912:
5904:
5899:
5894:
5889:
5884:
5882:
5879:
5871:
5866:
5861:
5856:
5851:
5849:
5846:
5838:
5833:
5828:
5823:
5818:
5816:
5813:
5805:
5800:
5795:
5790:
5785:
5783:
5780:
5772:
5767:
5762:
5757:
5752:
5750:
5739:
5734:
5729:
5724:
5719:
5717:
5707:
5703:
5696:
5688:
5683:
5678:
5673:
5668:
5666:
5663:
5655:
5650:
5645:
5640:
5635:
5633:
5623:
5618:
5613:
5608:
5603:
5601:
5599:
5594:
5589:
5584:
5579:
5574:
5572:
5568:
5560:
5556:
5549:
5541:
5536:
5531:
5526:
5521:
5519:
5516:
5508:
5503:
5498:
5493:
5488:
5486:
5483:
5475:
5470:
5465:
5460:
5455:
5453:
5450:
5442:
5437:
5432:
5427:
5422:
5420:
5410:
5405:
5400:
5395:
5390:
5385:
5380:
5378:
5376:
5371:
5366:
5361:
5356:
5351:
5349:
5345:
5338:
5334:
5321:
5315:
5303:
5281:
5276:
5271:
5266:
5261:
5259:
5250:
5242:
5237:
5232:
5230:
5227:
5219:
5214:
5209:
5207:
5204:
5196:
5191:
5186:
5184:
5173:
5168:
5163:
5161:
5151:
5147:
5139:
5131:
5126:
5121:
5119:
5109:
5104:
5099:
5097:
5095:
5090:
5085:
5080:
5078:
5074:
5066:
5062:
5054:
5046:
5041:
5036:
5034:
5024:
5019:
5014:
5012:
5002:
4998:
4991:
4983:
4978:
4973:
4968:
4963:
4958:
4953:
4951:
4948:
4940:
4935:
4930:
4925:
4920:
4915:
4910:
4908:
4905:
4897:
4892:
4887:
4882:
4877:
4872:
4867:
4865:
4862:
4854:
4849:
4844:
4839:
4834:
4829:
4824:
4822:
4812:
4807:
4802:
4797:
4792:
4790:
4788:
4783:
4778:
4773:
4768:
4763:
4758:
4753:
4751:
4747:
4740:
4736:
4729:
4721:
4716:
4711:
4706:
4701:
4696:
4691:
4689:
4686:
4678:
4673:
4668:
4663:
4658:
4653:
4648:
4646:
4645:
4642:
4634:
4629:
4624:
4619:
4614:
4609:
4604:
4602:
4599:
4591:
4586:
4581:
4576:
4571:
4566:
4561:
4559:
4556:
4548:
4543:
4538:
4533:
4528:
4523:
4518:
4516:
4513:
4505:
4500:
4495:
4490:
4485:
4480:
4475:
4473:
4463:
4458:
4453:
4448:
4443:
4438:
4433:
4431:
4422:
4418:
4405:
4399:
4387:
4361:
4356:
4351:
4346:
4341:
4336:
4331:
4329:
4326:
4318:
4303:
4293:
4278:
4266:
4255:
4244:
4233:
4222:
4211:
4200:
4191:
4182:
4171:
4160:
4149:
4138:
4127:
4116:
3957:
3952:
3947:
3942:
3940:
3939:
3934:
3929:
3924:
3919:
3914:
3912:
3911:
3907:
3895:
3890:
3885:
3880:
3878:
3877:
3872:
3867:
3862:
3857:
3852:
3850:
3849:
3845:
3833:
3828:
3823:
3818:
3813:
3811:
3810:
3806:
3794:
3789:
3784:
3782:
3781:
3776:
3771:
3766:
3761:
3756:
3754:
3753:
3749:
3737:
3732:
3727:
3722:
3717:
3715:
3714:
3710:
3698:
3693:
3688:
3686:
3685:
3680:
3675:
3670:
3665:
3660:
3658:
3657:
3653:
3641:
3636:
3631:
3626:
3621:
3619:
3618:
3614:
3602:
3597:
3592:
3587:
3582:
3580:
3579:
3576:
3511:
3506:
3501:
3496:
3491:
3486:
3484:
3483:
3478:
3473:
3468:
3463:
3458:
3453:
3448:
3446:
3445:
3434:
3429:
3424:
3419:
3414:
3409:
3407:
3406:
3401:
3396:
3391:
3386:
3381:
3376:
3371:
3369:
3368:
3358:
3353:
3348:
3343:
3338:
3333:
3328:
3326:
3325:
3315:
3310:
3305:
3300:
3295:
3290:
3285:
3283:
3282:
3277:
3272:
3267:
3262:
3257:
3255:
3254:
3249:
3244:
3239:
3234:
3229:
3224:
3219:
3217:
3216:
3206:
3201:
3196:
3191:
3186:
3181:
3176:
3174:
3173:
3163:
3158:
3153:
3148:
3143:
3138:
3133:
3128:
3126:
3125:
3120:
3115:
3110:
3105:
3100:
3098:
3097:
3092:
3087:
3082:
3077:
3072:
3067:
3062:
3060:
3059:
3049:
3044:
3039:
3034:
3029:
3024:
3019:
3017:
3016:
3006:
3001:
2996:
2991:
2986:
2981:
2976:
2974:
2973:
2900:
2895:
2890:
2885:
2880:
2878:
2877:
2873:
2861:
2856:
2851:
2846:
2841:
2839:
2838:
2834:
2822:
2817:
2812:
2807:
2802:
2800:
2799:
2795:
2783:
2778:
2773:
2768:
2763:
2761:
2760:
2756:
2744:
2739:
2734:
2729:
2724:
2722:
2721:
2717:
2705:
2700:
2695:
2690:
2685:
2683:
2682:
2678:
2666:
2661:
2656:
2651:
2646:
2644:
2643:
2639:
2568:
2563:
2558:
2553:
2548:
2543:
2538:
2533:
2531:
2530:
2525:
2520:
2515:
2510:
2505:
2500:
2495:
2490:
2488:
2487:
2482:
2477:
2472:
2467:
2462:
2460:
2459:
2454:
2449:
2444:
2439:
2434:
2429:
2424:
2422:
2421:
2410:
2405:
2400:
2395:
2390:
2385:
2380:
2375:
2373:
2372:
2367:
2362:
2357:
2352:
2347:
2342:
2337:
2332:
2330:
2329:
2324:
2319:
2314:
2309:
2304:
2302:
2301:
2296:
2291:
2286:
2281:
2276:
2271:
2266:
2264:
2263:
2253:
2248:
2243:
2238:
2233:
2231:
2230:
2225:
2220:
2215:
2210:
2205:
2200:
2195:
2193:
2192:
2182:
2177:
2172:
2167:
2162:
2157:
2152:
2150:
2149:
2144:
2139:
2134:
2129:
2124:
2119:
2114:
2112:
2111:
2106:
2101:
2096:
2091:
2086:
2084:
2083:
2078:
2073:
2068:
2063:
2058:
2053:
2048:
2046:
2045:
2035:
2030:
2025:
2020:
2015:
2013:
2012:
2007:
2002:
1997:
1992:
1987:
1982:
1977:
1975:
1974:
1964:
1959:
1954:
1949:
1944:
1939:
1934:
1929:
1927:
1926:
1921:
1916:
1911:
1906:
1901:
1896:
1891:
1886:
1884:
1883:
1878:
1873:
1868:
1863:
1858:
1856:
1855:
1850:
1845:
1840:
1835:
1830:
1825:
1820:
1818:
1817:
1807:
1802:
1797:
1792:
1787:
1785:
1784:
1779:
1774:
1769:
1764:
1759:
1754:
1749:
1747:
1746:
1665:Schläfli symbol
1654:
1565:cubic honeycomb
1561:
1535:
1530:
1525:
1520:
1515:
1510:
1505:
1503:
1497:
1492:
1487:
1482:
1477:
1472:
1467:
1462:
1460:
1435:
1430:
1425:
1420:
1415:
1410:
1405:
1400:
1398:
1380:
1370:
1365:
1360:
1355:
1350:
1345:
1340:
1335:
1330:
1328:
1304:
1299:
1294:
1289:
1284:
1279:
1274:
1269:
1267:
1265:
1260:
1255:
1250:
1245:
1240:
1235:
1230:
1225:
1220:
1218:
1205:
1195:
1190:
1185:
1183:
1177:
1175:
1158:
1148:
1143:
1138:
1133:
1128:
1123:
1118:
1116:
1110:
1108:
1086:
1081:
1076:
1071:
1066:
1061:
1056:
1054:
1048:
1043:
1038:
1033:
1028:
1026:
1020:
1018:
995:
990:
985:
980:
975:
970:
965:
963:
957:
952:
947:
942:
937:
932:
927:
922:
920:
919:
914:
909:
904:
899:
894:
889:
884:
882:
876:
874:
865:
860:Schläfli symbol
855:Coxeter diagram
848:
833:
820:
815:
810:
805:
800:
795:
790:
788:
778:
773:
768:
763:
758:
753:
748:
743:
738:
736:
729:
724:
719:
714:
709:
704:
699:
694:
689:
684:
679:
677:
670:Coxeter diagram
664:
656:
652:
647:
643:
639:
623:
619:
614:
609:
604:
599:
594:
545:
543:
538:
536:
531:
529:
524:
522:
517:
515:
510:
508:
492:
441:
425:
394:
322:Schläfli symbol
286:cubic honeycomb
258:
229:
218:
217:
216:
214:
211:
210:
199:
195:
188:
177:
132:
127:
122:
117:
112:
107:
102:
100:
96:Coxeter diagram
86:Schläfli symbol
80:
76:
72:
71:
67:
17:
12:
11:
5:
18601:
18591:
18590:
18585:
18580:
18575:
18559:
18558:
18554:
18547:
18540:
18536:
18529:
18527:
18524:
18517:
18515:
18512:
18505:
18503:
18500:
18497:
18493:
18483:
18479:
18478:
18476:
18472:
18470:
18468:
18464:
18462:
18460:
18456:
18454:
18452:
18450:
18447:
18444:
18440:
18439:
18437:
18433:
18431:
18429:
18425:
18423:
18421:
18417:
18415:
18413:
18411:
18408:
18403:
18399:
18398:
18394:
18387:
18380:
18376:
18372:
18370:
18368:
18363:
18361:
18358:
18353:
18351:
18348:
18345:
18341:
18336:
18332:
18331:
18327:
18320:
18316:
18311:
18309:
18306:
18301:
18299:
18296:
18291:
18289:
18286:
18283:
18279:
18274:
18270:
18269:
18265:
18261:
18256:
18254:
18251:
18246:
18244:
18241:
18236:
18234:
18231:
18228:
18224:
18219:
18215:
18214:
18212:
18207:
18205:
18202:
18197:
18195:
18192:
18187:
18185:
18182:
18179:
18175:
18170:
18166:
18165:
18160:
18155:
18153:
18150:
18145:
18143:
18140:
18135:
18133:
18130:
18127:
18123:
18118:
18114:
18113:
18111:
18106:
18104:
18101:
18096:
18094:
18091:
18086:
18084:
18081:
18078:
18074:
18069:
18065:
18064:
18059:
18054:
18052:
18049:
18044:
18042:
18039:
18034:
18032:
18029:
18026:
18022:
18020:Uniform tiling
18017:
18013:
18012:
17999:
17996:
17993:
17986:
17983:
17957:
17950:
17947:
17921:
17914:
17911:
17897:
17884:
17881:
17878:
17871:
17868:
17854:
17841:
17838:
17835:
17828:
17825:
17811:
17798:
17795:
17792:
17785:
17782:
17768:
17755:
17752:
17749:
17742:
17739:
17725:
17720:
17716:
17715:
17704:
17702:
17701:
17694:
17687:
17679:
17674:
17673:
17668:
17659:
17649:
17648:
17647:
17625:
17622:Geombinatorics
17615:
17605:
17586:
17567:John H. Conway
17561:
17560:
17549:
17540:
17525:
17515:
17514:
17512:
17509:
17508:
17507:
17502:
17497:
17491:
17486:
17481:
17474:
17471:
17382:
17381:
17380:, non-uniform
17375:
17371:
17370:
17368:
17362:
17361:
17354:
17350:
17349:
17338:
17334:
17333:
17314:
17310:
17309:
17212:
17206:
17205:
17201:
17195:
17192:
17186:
17185:
17180:
17176:
17175:
17168:
17165:
17109:
17108:
17103:
17099:
17098:
17086:
17082:
17081:
17078:
17072:
17071:
17060:
17056:
17055:
17036:
17032:
17031:
16934:
16928:
16927:
16922:
16916:
16915:
16910:
16906:
16905:
16898:
16895:
16839:
16838:
16833:
16829:
16828:
16816:
16812:
16811:
16809:
16803:
16802:
16791:
16787:
16786:
16767:
16763:
16762:
16665:
16659:
16658:
16654:
16648:
16645:
16639:
16638:
16633:
16629:
16628:
16621:
16618:
16611:
16596:
16540:
16539:
16538:, non-uniform
16533:
16529:
16528:
16520:
16516:
16515:
16512:
16506:
16505:
16492:
16486:
16485:
16474:
16470:
16469:
16450:
16446:
16442:
16441:
16402:
16396:
16395:
16391:
16388:
16382:
16381:
16376:
16372:
16371:
16364:
16361:
16354:
16343:
16324:
16264:
16263:
16262:, non-uniform
16257:
16253:
16252:
16244:
16240:
16239:
16237:
16231:
16230:
16223:
16219:
16218:
16207:
16203:
16202:
16165:
16161:
16157:
16156:
16117:
16111:
16110:
16106:
16103:
16097:
16096:
16091:
16087:
16086:
16079:
16076:
16072:
16071:
16064:
16057:
16050:
16042:
16041:
16034:
16027:
16020:
16002:
16001:
15973:
15972:
15967:
15963:
15962:
15957:
15953:
15952:
15949:
15943:
15942:
15929:
15928:Vertex figures
15925:
15924:
15917:
15913:
15912:
15873:
15867:
15866:
15862:
15859:
15853:
15852:
15849:
15845:
15844:
15837:
15834:
15754:
15753:
15752:, non-uniform
15747:
15743:
15742:
15737:
15733:
15732:
15729:
15723:
15722:
15710:
15706:
15705:
15694:
15690:
15689:
15661:
15657:
15656:
15617:
15611:
15610:
15606:
15603:
15597:
15596:
15591:
15587:
15586:
15579:
15576:
15513:
15491:
15488:
15485:
15484:
15477:
15469:
15468:
15459:
15435:
15432:
15429:
15428:
15421:
15414:
15408:
15407:
15388:
15349:
15343:
15342:
15335:
15328:
15324:
15323:
15320:
15317:
15311:
15310:
15303:
15296:
15290:
15289:
15275:
15268:
15265:
15251:
15237:
15230:
15227:
15213:
15186:
15183:
15180:
15179:
15172:
15165:
15158:
15154:
15153:
15146:
15139:
15132:
15128:
15127:
15124:
15121:
15118:
15101:
15098:
15097:
15096:
15032:
15031:
15026:
15022:
15021:
15009:
15005:
15004:
14991:
14984:
14981:
14966:
14960:
14959:
14946:
14936:Symmetry group
14932:
14931:
14920:
14914:
14913:
14897:
14893:
14892:
14873:
14869:
14868:
14829:
14823:
14822:
14818:
14815:
14809:
14808:
14803:
14799:
14798:
14791:
14788:
14751:
14729:
14726:
14725:
14724:
14699:
14692:
14689:
14624:
14621:
14620:
14619:
14594:
14591:
14588:
14587:
14580:
14573:
14566:
14562:
14561:
14554:
14547:
14540:
14536:
14535:
14532:
14529:
14526:
14509:
14506:
14503:
14502:
14495:
14488:
14481:
14357:
14356:
14351:
14347:
14346:
14334:
14330:
14329:
14320:
14310:
14309:
14296:
14289:
14286:
14271:
14265:
14264:
14250:
14244:
14243:
14227:
14223:
14222:
14185:
14181:
14180:
14141:
14135:
14134:
14130:
14127:
14121:
14120:
14115:
14111:
14110:
14103:
14100:
14067:
14049:
14046:
14040:
14029:
14018:
13950:
13949:
13948:, non-uniform
13943:
13939:
13938:
13930:
13926:
13925:
13923:
13917:
13916:
13909:
13903:
13902:
13891:
13887:
13886:
13858:
13854:
13850:
13849:
13810:
13804:
13803:
13799:
13796:
13790:
13789:
13784:
13780:
13779:
13772:
13769:
13765:
13764:
13719:
13587:
13564:
13563:
13562:, non-uniform
13557:
13553:
13552:
13506:
13502:
13501:
13499:
13493:
13492:
13480:
13474:
13473:
13462:
13458:
13457:
13429:
13425:
13424:
13319:
13313:
13312:
13307:
13301:
13300:
13295:
13291:
13290:
13283:
13280:
13243:
13221:
13218:
13215:
13214:
13207:
13182:
13179:
13178:
13177:
13152:
13145:
13142:
13076:
13073:
13070:
13069:
13065:
13061:
13053:
13052:
13045:
13038:
13032:
13031:
13002:
12963:
12957:
12956:
12949:
12942:
12938:
12937:
12934:
12931:
12925:
12924:
12917:
12910:
12904:
12903:
12890:
12883:
12880:
12865:
12850:
12843:
12840:
12825:
12819:
12818:
12815:
12812:
12794:
12791:
12788:
12787:
12780:
12773:
12766:
12762:
12761:
12754:
12747:
12740:
12736:
12735:
12732:
12729:
12726:
12709:
12706:
12705:
12704:
12692:
12689:
12688:
12687:
12619:
12618:
12613:
12609:
12608:
12596:
12592:
12591:
12582:
12576:Symmetry group
12572:
12571:
12558:
12551:
12548:
12533:
12527:
12526:
12510:
12504:
12503:
12487:
12483:
12482:
12454:
12450:
12449:
12344:
12338:
12337:
12331:
12330:tr{4,3,4} or t
12328:
12322:
12321:
12316:
12312:
12311:
12304:
12301:
12300:
12299:
12231:
12228:
12186:
12183:
12180:
12179:
12175:
12171:
12163:
12162:
12155:
12148:
12142:
12141:
12134:
12127:
12123:
12122:
12093:
12054:
12048:
12047:
12040:
12033:
12027:
12026:
12013:
12006:
12003:
11988:
11973:
11966:
11963:
11948:
11942:
11941:
11938:
11935:
11923:Coxeter groups
11914:
11911:
11908:
11907:
11900:
11893:
11886:
11882:
11881:
11874:
11867:
11860:
11856:
11855:
11852:
11849:
11846:
11829:
11826:
11823:
11822:
11809:
11798:
11795:
11794:
11793:
11726:
11725:
11720:
11716:
11715:
11703:
11699:
11698:
11685:
11678:
11675:
11660:
11654:
11653:
11644:
11634:
11633:
11622:
11618:
11617:
11589:
11585:
11584:
11479:
11473:
11472:
11466:
11465:rr{4,3,4} or t
11463:
11457:
11456:
11451:
11447:
11446:
11439:
11436:
11432:
11431:
11428:
11423:
11420:
11417:
11414:
11410:
11409:
11380:
11361:
11332:
11293:
11274:
11268:
11267:
11265:
11262:
11260:
11258:
11255:
11249:
11248:
11245:
11242:
11239:
11236:
11233:
11227:
11226:
11223:
11216:
11209:
11202:
11195:
11065:
11064:
11063:, non-uniform
11058:
11054:
11053:
11041:
11037:
11036:
11023:
11016:
11013:
10998:
10992:
10991:
10984:
10980:
10979:
10973:
10969:
10968:
10949:
10945:
10944:
10707:
10701:
10700:
10693:
10687:
10686:
10681:
10677:
10676:
10669:
10666:
10643:
10617:
10603:
10600:
10597:
10596:
10589:
10582:
10575:
10568:
10561:
10553:
10552:
10548:
10544:
10540:
10536:
10532:
10524:
10523:
10516:
10509:
10502:
10495:
10488:
10482:
10481:
10466:
10439:
10418:
10403:
10394:
10388:
10387:
10368:
10339:
10310:
10271:
10252:
10246:
10245:
10209:
10202:
10199:
10185:
10141:
10134:
10131:
10117:
10045:
10038:
10035:
10021:
9949:
9942:
9939:
9925:
9851:
9844:
9841:
9827:
9821:
9820:
9817:
9814:
9811:
9808:
9805:
9799:
9798:
9791:
9784:
9777:
9770:
9763:
9745:Coxeter groups
9727:
9720:
9717:
9689:
9686:
9683:
9682:
9675:
9668:
9661:
9654:
9647:
9643:
9642:
9635:
9628:
9621:
9614:
9607:
9603:
9602:
9599:
9596:
9593:
9564:
9561:
9458:
9457:
9447:
9443:
9442:
9428:
9424:
9423:
9409:
9402:
9399:
9385:
9379:
9378:
9365:
9355:Symmetry group
9351:
9350:
9339:
9333:
9332:
9326:
9320:
9319:
9308:
9304:
9303:
9293:
9289:
9288:
9249:
9243:
9242:
9238:
9233:
9227:
9226:
9221:
9217:
9216:
9202:
9201:
9194:
9191:
9155:
9152:
9149:
9148:
9141:
9134:
9128:
9127:
9088:
9021:
9015:
9014:
9007:
9000:
8996:
8995:
8988:
8981:
8975:
8974:
8959:
8952:
8949:
8934:
8921:
8914:
8911:
8896:
8890:
8889:
8886:
8883:
8874:Coxeter groups
8865:
8862:
8859:
8858:
8851:
8844:
8837:
8833:
8832:
8825:
8818:
8811:
8807:
8806:
8803:
8800:
8797:
8780:
8777:
8744:square pyramid
8714:
8713:
8708:
8704:
8703:
8691:
8687:
8686:
8672:
8665:
8662:
8648:
8642:
8641:
8632:
8622:
8621:
8619:square pyramid
8609:
8603:
8602:
8591:
8587:
8586:
8567:
8563:
8562:
8457:
8451:
8450:
8444:
8441:
8435:
8434:
8429:
8425:
8424:
8417:
8414:
8385:
8382:
8381:
8380:
8366:{2,6,3}, with
8363:
8362:, and symbol s
8304:
8303:
8295:
8292:
8284:
8281:
8273:
8270:
8262:
8259:
8251:
8250:
8243:
8236:
8229:
8222:
8216:
8215:
8186:
8157:
8127:
8126:
8087:
8048:
8009:
7970:
7962:
7961:
7954:
7947:
7940:
7933:
7929:
7928:
7919:
7910:
7901:
7892:
7886:
7885:
7872:
7865:
7862:
7846:
7833:
7826:
7823:
7807:
7794:
7787:
7784:
7768:
7755:
7748:
7745:
7730:
7717:name, and the
7702:
7699:
7696:
7695:
7688:
7681:
7674:
7670:
7669:
7662:
7655:
7648:
7644:
7643:
7640:
7637:
7634:
7617:
7614:
7551:
7550:
7541:
7537:
7536:
7524:
7520:
7519:
7505:
7498:
7495:
7481:
7475:
7474:
7465:
7455:
7454:
7443:
7437:
7436:
7425:
7421:
7420:
7401:
7397:
7396:
7103:
7097:
7096:
7086:
7083:
7077:
7076:
7071:
7067:
7066:
7059:
7056:
7052:
7051:
7046:
7026:
7012:
7005:
7002:
6974:
6967:
6964:
6950:
6945:
6942:
6932:
6931:
6926:
6906:
6892:
6885:
6882:
6854:
6847:
6844:
6829:
6791:
6786:
6778:
6775:
6766:
6765:
6760:
6730:
6717:
6710:
6707:
6690:
6676:
6669:
6666:
6652:
6584:
6579:
6571:
6568:
6558:
6557:
6552:
6532:
6529:
6515:
6508:
6505:
6491:
6433:
6428:
6420:
6417:
6407:
6406:
6401:
6367:
6337:
6324:
6317:
6314:
6297:
6283:
6276:
6273:
6259:
6201:
6196:
6188:
6185:
6175:
6174:
6171:
6158:
6151:
6148:
6134:
6105:
6103:
6095:
6092:
6082:
6081:
6078:
6073:
6068:
6061:
6054:
6049:
6041:
6040:
6039:A3 honeycombs
6013:
6006:
6003:
5982:
5981:
5976:
5943:
5910:
5877:
5844:
5811:
5778:
5747:
5744:
5715:
5712:
5709:
5699:
5698:
5694:
5661:
5631:
5628:
5570:
5565:
5562:
5552:
5551:
5547:
5514:
5481:
5448:
5418:
5415:
5347:
5343:
5340:
5330:
5329:
5326:
5323:
5318:
5311:
5306:
5298:
5297:
5296:B3 honeycombs
5254:
5253:
5248:
5225:
5202:
5181:
5178:
5159:
5156:
5153:
5143:
5142:
5137:
5117:
5114:
5076:
5071:
5068:
5058:
5057:
5052:
5032:
5029:
5010:
5007:
5004:
4994:
4993:
4989:
4946:
4903:
4860:
4820:
4817:
4749:
4745:
4742:
4732:
4731:
4727:
4684:
4640:
4597:
4554:
4511:
4471:
4468:
4429:
4427:
4424:
4414:
4413:
4410:
4407:
4402:
4395:
4390:
4382:
4381:
4380:C3 honeycombs
4325:
4322:
4316:
4291:
4277:
4274:
4271:
4270:
4259:
4248:
4237:
4226:
4215:
4204:
4193:
4187:
4186:
4175:
4164:
4153:
4142:
4131:
4120:
4109:
4105:
4104:
4097:
4090:
4083:
4076:
4069:
4062:
4055:
4051:
4050:
4044:
4039:
4034:
4029:
4024:
4019:
4014:
4010:
4009:
4006:
4003:
4000:
3997:
3994:
3990:
3989:
3984:
3981:
3976:
3972:
3971:
3963:
3962:
3900:
3838:
3799:
3742:
3703:
3646:
3607:
3571:
3570:
3563:
3556:
3549:
3542:
3535:
3528:
3521:
3517:
3516:
3439:
3363:
3320:
3211:
3168:
3054:
3011:
2969:
2968:
2965:
2962:
2959:
2956:
2953:
2949:
2948:
2943:
2938:
2933:
2929:
2928:
2906:
2905:
2866:
2827:
2788:
2749:
2710:
2671:
2632:
2628:
2627:
2620:
2613:
2606:
2599:
2592:
2585:
2578:
2574:
2573:
2415:
2258:
2187:
2040:
1969:
1812:
1741:
1737:
1736:
1733:
1730:
1727:
1724:
1721:
1717:
1716:
1711:
1706:
1701:
1697:
1696:
1687:vertex figures
1653:
1650:
1647:
1646:
1639:
1632:
1625:
1621:
1620:
1613:
1606:
1599:
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1540:
1458:
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1450:
1443:
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1396:
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1392:
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1326:
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1181:
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1114:
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1094:
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1014:
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880:
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867:
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829:
826:
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783:
734:
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637:
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512:
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501:
496:
489:
483:
477:
475:Parallelepiped
472:
466:
465:
460:
455:
450:
445:
436:
434:Crystal system
424:
421:
393:
390:
380:. Any finite
280:
279:
270:
266:
265:
253:
247:
246:
232:
225:
222:
208:
202:
201:
192:
182:
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170:
164:
163:
157:
153:
152:
142:
138:
137:
98:
92:
91:
88:
82:
81:
78:
74:
69:
65:
62:
58:
57:
52:
48:
47:
42:
38:
37:
24:
23:
15:
9:
6:
4:
3:
2:
18600:
18589:
18586:
18584:
18581:
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18576:
18574:
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18570:
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18550:
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18508:
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18477:
18469:
18461:
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18445:
18442:
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18438:
18430:
18422:
18414:
18409:
18407:
18404:
18401:
18400:
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18390:
18383:
18377:
18369:
18367:
18359:
18357:
18349:
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18342:
18340:
18337:
18334:
18333:
18330:
18323:
18317:
18315:
18307:
18305:
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18275:
18272:
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18213:
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18176:
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18141:
18139:
18131:
18129:
18124:
18122:
18119:
18116:
18115:
18112:
18110:
18102:
18100:
18092:
18090:
18082:
18080:
18075:
18073:
18070:
18067:
18066:
18063:
18060:
18058:
18050:
18048:
18040:
18038:
18030:
18028:
18023:
18021:
18018:
18015:
18014:
17997:
17994:
17991:
17981:
17955:
17945:
17919:
17909:
17898:
17882:
17879:
17876:
17866:
17855:
17839:
17836:
17833:
17823:
17812:
17796:
17793:
17790:
17780:
17769:
17753:
17750:
17747:
17737:
17726:
17724:
17721:
17718:
17717:
17712:
17708:
17700:
17695:
17693:
17688:
17686:
17681:
17680:
17677:
17672:
17669:
17665:
17660:
17657:
17653:
17650:
17645:
17641:
17640:
17639:
17637:
17633:
17629:
17626:
17623:
17619:
17616:
17614:
17610:
17606:
17603:
17602:0-486-61480-8
17599:
17595:
17594:
17590:
17587:
17584:
17580:
17576:
17572:
17568:
17565:
17564:
17558:
17553:
17544:
17537:
17533:
17529:
17520:
17516:
17506:
17503:
17501:
17498:
17495:
17492:
17490:
17487:
17485:
17482:
17480:
17477:
17476:
17470:
17467:
17465:
17461:
17457:
17453:
17449:
17397:
17393:
17389:
17379:
17376:
17372:
17369:
17367:
17363:
17359:
17355:
17353:Vertex figure
17351:
17347:
17342:
17339:
17335:
17331:
17327:
17322:
17318:
17315:
17311:
17213:
17211:
17207:
17193:
17191:
17187:
17184:
17181:
17177:
17172:
17163:
17161:
17156:
17154:
17149:
17147:
17142:
17140:
17136:
17132:
17128:
17124:
17120:
17116:
17107:
17104:
17100:
17096:
17090:
17087:
17083:
17079:
17077:
17076:Coxeter group
17073:
17069:
17064:
17061:
17057:
17053:
17049:
17044:
17040:
17037:
17033:
16935:
16933:
16929:
16923:
16921:
16917:
16914:
16911:
16907:
16902:
16893:
16891:
16886:
16884:
16879:
16877:
16872:
16870:
16866:
16862:
16858:
16854:
16850:
16846:
16837:
16834:
16830:
16826:
16820:
16817:
16813:
16810:
16808:
16807:Coxeter group
16804:
16800:
16795:
16792:
16788:
16784:
16780:
16775:
16771:
16768:
16764:
16666:
16664:
16660:
16646:
16644:
16640:
16637:
16634:
16630:
16625:
16616:
16614:
16607:
16603:
16599:
16592:
16551:
16547:
16537:
16534:
16530:
16526:
16521:
16517:
16513:
16511:
16510:Coxeter group
16507:
16503:
16497:
16493:
16491:
16490:Vertex figure
16487:
16483:
16478:
16475:
16471:
16467:
16463:
16458:
16454:
16447:
16443:
16403:
16401:
16397:
16389:
16387:
16383:
16380:
16377:
16373:
16368:
16359:
16357:
16350:
16346:
16339:
16335:
16331:
16327:
16320:
16279:
16275:
16271:
16261:
16258:
16254:
16250:
16245:
16241:
16238:
16236:
16235:Coxeter group
16232:
16228:
16224:
16222:Vertex figure
16220:
16216:
16211:
16208:
16204:
16200:
16196:
16191:
16187:
16182:
16178:
16173:
16169:
16162:
16158:
16118:
16116:
16112:
16104:
16102:
16098:
16095:
16092:
16088:
16083:
16069:
16065:
16062:
16058:
16055:
16051:
16048:
16044:
16043:
16039:
16035:
16032:
16028:
16025:
16021:
16016:
16012:
16005:
15999:
15995:
15994:
15993:
15991:
15986:
15984:
15980:
15971:
15968:
15964:
15961:
15958:
15954:
15950:
15948:
15944:
15941:
15937:
15933:
15930:
15926:
15922:
15918:
15914:
15874:
15872:
15868:
15860:
15858:
15854:
15850:
15846:
15841:
15833:
15831:
15827:
15823:
15819:
15815:
15773:
15769:
15765:
15761:
15751:
15748:
15744:
15741:
15738:
15734:
15730:
15728:
15724:
15720:
15715:
15711:
15709:Vertex figure
15707:
15703:
15698:
15695:
15691:
15687:
15683:
15678:
15674:
15669:
15665:
15662:
15658:
15618:
15616:
15612:
15604:
15602:
15598:
15595:
15592:
15588:
15583:
15574:
15573:
15572:Vertex figure
15568:
15563:
15561:
15557:
15553:
15549:
15544:
15543:
15538:
15533:
15532:
15531:Vertex figure
15527:
15522:
15520:
15516:
15509:
15505:
15501:
15497:
15482:
15478:
15475:
15471:
15470:
15466:
15460:
15457:
15451:
15450:
15447:
15445:
15441:
15426:
15422:
15419:
15415:
15413:
15412:Vertex figure
15410:
15389:
15350:
15348:
15345:
15344:
15340:
15336:
15333:
15329:
15326:
15321:
15318:
15316:
15313:
15312:
15304:
15297:
15295:
15292:
15291:
15273:
15263:
15252:
15235:
15225:
15214:
15212:
15209:
15208:
15202:
15200:
15196:
15192:
15177:
15173:
15170:
15166:
15163:
15159:
15156:
15155:
15151:
15147:
15144:
15140:
15137:
15133:
15130:
15129:
15122:
15119:
15116:
15115:
15109:
15107:
15094:
15088:
15084:
15083:
15082:
15080:
15076:
15072:
15068:
15066:
15065:vertex figure
15063:
15059:
15055:
15051:
15047:
15043:
15039:
15030:
15027:
15023:
15019:
15013:
15010:
15006:
14989:
14979:
14967:
14965:
14964:Coxeter group
14961:
14954:
14947:
14945:
14941:
14937:
14933:
14930:
14925:
14921:
14919:
14918:Vertex figure
14915:
14911:
14906:
14901:
14898:
14894:
14890:
14886:
14881:
14877:
14874:
14870:
14830:
14828:
14824:
14816:
14814:
14810:
14807:
14804:
14800:
14795:
14786:
14785:
14780:
14775:
14774:
14773:Vertex figure
14769:
14764:
14762:
14758:
14754:
14747:
14743:
14739:
14735:
14722:
14718:
14717:
14716:
14713:
14697:
14687:
14638:
14634:
14630:
14617:
14612:
14608:
14607:
14606:
14604:
14600:
14585:
14581:
14578:
14574:
14571:
14567:
14564:
14563:
14559:
14555:
14552:
14548:
14545:
14541:
14538:
14537:
14530:
14527:
14524:
14523:
14517:
14515:
14500:
14496:
14493:
14489:
14486:
14482:
14479:
14475:
14474:
14471:
14469:
14465:
14461:
14457:
14455:
14451:
14409:
14404:
14402:
14401:vertex figure
14399:
14396:
14392:
14388:
14384:
14380:
14376:
14372:
14369:is a uniform
14368:
14364:
14355:
14352:
14348:
14344:
14338:
14335:
14331:
14321:
14319:
14315:
14311:
14294:
14284:
14272:
14270:
14269:Coxeter group
14266:
14263:
14260:
14255:
14251:
14249:
14248:Vertex figure
14245:
14241:
14236:
14231:
14228:
14224:
14220:
14216:
14211:
14207:
14202:
14198:
14193:
14189:
14186:
14182:
14142:
14140:
14136:
14128:
14126:
14122:
14119:
14116:
14112:
14107:
14098:
14097:
14092:
14087:
14086:
14085:Vertex figure
14081:
14076:
14074:
14070:
14063:
14059:
14055:
14045:
14043:
14036:
14032:
14025:
14021:
14014:
13973:
13969:
13965:
13961:
13957:
13947:
13944:
13940:
13936:
13931:
13927:
13924:
13922:
13921:Coxeter group
13918:
13914:
13910:
13908:
13907:Vertex figure
13904:
13900:
13895:
13892:
13888:
13884:
13880:
13875:
13871:
13866:
13862:
13855:
13851:
13811:
13809:
13805:
13797:
13795:
13791:
13788:
13785:
13781:
13776:
13724:
13720:
13679:
13675:
13671:
13667:
13600:
13594:
13590:
13583:
13579:
13575:
13571:
13561:
13558:
13554:
13550:
13507:
13503:
13500:
13498:
13497:Coxeter group
13494:
13490:
13485:
13481:
13479:
13478:Vertex figure
13475:
13471:
13466:
13463:
13459:
13455:
13451:
13446:
13442:
13437:
13433:
13430:
13426:
13320:
13318:
13314:
13308:
13306:
13302:
13299:
13296:
13292:
13287:
13278:
13277:
13272:
13267:
13266:
13265:Vertex figure
13261:
13256:
13254:
13250:
13246:
13239:
13235:
13231:
13227:
13212:
13208:
13205:
13201:
13200:
13194:
13192:
13188:
13175:
13171:
13170:
13169:
13166:
13150:
13140:
13090:
13086:
13082:
13066:
13062:
13055:
13050:
13046:
13043:
13039:
13037:
13036:Vertex figure
13034:
13033:
13003:
12964:
12962:
12959:
12958:
12954:
12950:
12947:
12943:
12940:
12935:
12932:
12930:
12927:
12926:
12918:
12911:
12909:
12906:
12905:
12888:
12878:
12866:
12848:
12838:
12826:
12824:
12823:Coxeter group
12821:
12816:
12813:
12811:Construction
12810:
12809:
12806:
12804:
12800:
12785:
12781:
12778:
12774:
12771:
12767:
12764:
12763:
12759:
12755:
12752:
12748:
12745:
12741:
12738:
12737:
12730:
12727:
12724:
12723:
12717:
12715:
12702:
12698:
12697:
12696:
12685:
12679:
12675:
12674:
12673:
12671:
12667:
12663:
12659:
12657:
12656:vertex figure
12654:
12650:
12646:
12642:
12638:
12634:
12630:
12626:
12617:
12614:
12610:
12606:
12600:
12597:
12593:
12583:
12581:
12577:
12573:
12556:
12546:
12534:
12532:
12531:Coxeter group
12528:
12525:
12520:
12515:
12511:
12509:
12508:Vertex figure
12505:
12501:
12496:
12491:
12488:
12484:
12480:
12476:
12471:
12467:
12462:
12458:
12455:
12451:
12345:
12343:
12339:
12329:
12327:
12323:
12320:
12317:
12313:
12308:
12297:
12293:
12292:
12291:
12288:
12249:
12245:
12241:
12237:
12226:
12224:
12220:
12216:
12212:
12208:
12204:
12200:
12199:cuboctahedron
12196:
12192:
12176:
12172:
12165:
12160:
12156:
12153:
12149:
12147:
12146:Vertex figure
12144:
12143:
12139:
12135:
12132:
12128:
12125:
12094:
12055:
12053:
12050:
12049:
12041:
12034:
12032:
12029:
12028:
12011:
12001:
11989:
11971:
11961:
11949:
11947:
11946:Coxeter group
11944:
11939:
11936:
11934:Construction
11933:
11932:
11926:
11924:
11920:
11905:
11901:
11898:
11894:
11891:
11887:
11884:
11883:
11879:
11875:
11872:
11868:
11865:
11861:
11858:
11857:
11850:
11847:
11844:
11843:
11837:
11835:
11820:
11814:
11810:
11807:
11803:
11791:
11786:
11782:
11781:
11780:
11778:
11774:
11770:
11766:
11764:
11763:vertex figure
11761:
11757:
11753:
11749:
11745:
11741:
11737:
11733:
11724:
11721:
11717:
11713:
11707:
11704:
11700:
11683:
11673:
11661:
11659:
11658:Coxeter group
11655:
11645:
11643:
11639:
11635:
11632:
11627:
11623:
11621:Vertex figure
11619:
11615:
11611:
11606:
11602:
11597:
11593:
11590:
11586:
11480:
11478:
11474:
11464:
11462:
11458:
11455:
11452:
11448:
11443:
11429:
11424:
11421:
11418:
11415:
11412:
11381:
11362:
11333:
11294:
11275:
11273:
11270:
11266:
11263:
11261:
11259:
11256:
11254:
11253:Coxeter group
11251:
11250:
11246:
11243:
11240:
11237:
11234:
11232:
11229:
11228:
11224:
11217:
11210:
11203:
11196:
11194:
11191:
11190:
11184:
11182:
11177:
11081:
11076:
11072:
11062:
11059:
11055:
11051:
11045:
11042:
11038:
11021:
11011:
10999:
10997:
10996:Coxeter group
10993:
10989:
10985:
10983:Vertex figure
10981:
10977:
10974:
10970:
10966:
10962:
10957:
10953:
10950:
10946:
10708:
10706:
10702:
10694:
10692:
10688:
10685:
10682:
10678:
10673:
10664:
10662:
10658:
10654:
10650:
10646:
10639:
10635:
10631:
10626:
10624:
10620:
10613:
10609:
10594:
10590:
10587:
10583:
10580:
10576:
10573:
10569:
10566:
10562:
10555:
10554:
10549:
10545:
10541:
10537:
10533:
10526:
10521:
10517:
10514:
10510:
10507:
10503:
10500:
10496:
10493:
10489:
10487:
10486:Vertex figure
10484:
10479:
10473:
10467:
10464:
10458:
10452:
10446:
10440:
10437:
10431:
10425:
10419:
10416:
10410:
10404:
10401:
10395:
10393:
10390:
10369:
10340:
10311:
10272:
10253:
10251:
10248:
10247:
10207:
10197:
10186:
10139:
10129:
10118:
10043:
10033:
10022:
9947:
9937:
9926:
9849:
9839:
9828:
9826:
9825:Coxeter group
9818:
9815:
9812:
9809:
9806:
9804:
9801:
9800:
9792:
9785:
9778:
9771:
9764:
9762:
9759:
9758:
9752:
9750:
9746:
9742:
9741:Coxeter group
9725:
9715:
9703:
9699:
9695:
9680:
9676:
9673:
9669:
9666:
9662:
9659:
9655:
9652:
9648:
9645:
9644:
9640:
9636:
9633:
9629:
9626:
9622:
9619:
9615:
9612:
9608:
9605:
9604:
9597:
9594:
9591:
9590:
9584:
9582:
9578:
9574:
9570:
9560:
9558:
9554:
9550:
9546:
9542:
9538:
9534:
9530:
9526:
9524:
9520:
9516:
9513:. It is also
9512:
9508:
9504:
9503:vertex figure
9501:
9497:
9493:
9489:
9485:
9481:
9477:
9473:
9464:
9455:
9451:
9448:
9444:
9440:
9434:
9429:
9425:
9407:
9397:
9386:
9384:
9383:Coxeter group
9380:
9373:
9366:
9364:
9360:
9356:
9352:
9349:
9344:
9340:
9338:
9337:Vertex figure
9334:
9330:
9327:
9325:
9321:
9317:
9312:
9309:
9305:
9301:
9297:
9294:
9290:
9250:
9248:
9244:
9234:
9232:
9228:
9225:
9222:
9218:
9214:
9208:
9203:
9198:
9189:
9188:
9183:
9178:
9177:
9176:Vertex figure
9172:
9167:
9165:
9161:
9146:
9142:
9139:
9135:
9133:
9132:Vertex figure
9130:
9089:
9022:
9020:
9017:
9012:
9008:
9005:
9001:
8998:
8989:
8982:
8980:
8977:
8976:
8957:
8947:
8935:
8919:
8909:
8897:
8895:
8894:Coxeter group
8892:
8887:
8884:
8882:Construction
8881:
8880:
8877:
8875:
8871:
8856:
8852:
8849:
8845:
8842:
8838:
8835:
8834:
8830:
8826:
8823:
8819:
8816:
8812:
8809:
8808:
8801:
8798:
8795:
8794:
8788:
8786:
8776:
8774:
8769:
8764:
8762:
8758:
8754:
8750:
8748:
8747:vertex figure
8745:
8741:
8737:
8733:
8729:
8725:
8721:
8712:
8709:
8705:
8701:
8695:
8692:
8688:
8670:
8660:
8649:
8647:
8646:Coxeter group
8643:
8633:
8631:
8627:
8623:
8620:
8614:
8610:
8608:
8607:Vertex figure
8604:
8600:
8595:
8592:
8588:
8584:
8580:
8575:
8571:
8568:
8564:
8458:
8456:
8452:
8443:t{4,3,4} or t
8442:
8440:
8436:
8433:
8430:
8426:
8421:
8412:
8411:
8406:
8401:
8399:
8395:
8391:
8377:
8373:
8372:
8371:
8369:
8323:
8319:
8315:
8311:
8293:
8282:
8271:
8260:
8253:
8248:
8244:
8241:
8237:
8234:
8230:
8227:
8223:
8221:
8220:Vertex figure
8218:
8187:
8158:
8129:
8088:
8049:
8010:
7969:
7959:
7955:
7952:
7948:
7945:
7941:
7938:
7934:
7931:
7920:
7911:
7902:
7893:
7891:
7888:
7887:
7870:
7860:
7847:
7831:
7821:
7808:
7792:
7782:
7769:
7753:
7743:
7731:
7729:
7726:
7722:
7720:
7716:
7712:
7711:Coxeter group
7708:
7693:
7689:
7686:
7682:
7679:
7675:
7672:
7671:
7667:
7663:
7660:
7656:
7653:
7649:
7646:
7645:
7638:
7635:
7632:
7631:
7625:
7623:
7613:
7611:
7606:
7601:
7599:
7595:
7591:
7587:
7585:
7584:vertex figure
7582:
7578:
7574:
7570:
7566:
7562:
7558:
7549:
7545:
7542:
7538:
7534:
7528:
7525:
7521:
7503:
7493:
7482:
7480:
7479:Coxeter group
7476:
7466:
7464:
7460:
7456:
7453:
7448:
7444:
7442:
7441:Vertex figure
7438:
7434:
7429:
7426:
7422:
7418:
7414:
7409:
7405:
7402:
7398:
7104:
7102:
7098:
7085:r{4,3,4} or t
7084:
7082:
7078:
7075:
7072:
7068:
7063:
7049:
7027:
7010:
7000:
6972:
6962:
6951:
6946:
6943:
6934:
6933:
6929:
6907:
6890:
6880:
6852:
6842:
6830:
6787:
6784:
6776:
6768:
6767:
6763:
6731:
6715:
6705:
6674:
6664:
6653:
6585:
6580:
6577:
6572:
6569:
6560:
6559:
6555:
6533:
6513:
6503:
6492:
6434:
6429:
6426:
6421:
6418:
6409:
6408:
6404:
6370:
6338:
6322:
6312:
6281:
6271:
6260:
6202:
6197:
6194:
6189:
6186:
6177:
6176:
6172:
6156:
6146:
6135:
6106:
6104:
6101:
6096:
6093:
6084:
6083:
6079:
6074:
6069:
6067:
6062:
6060:
6055:
6053:
6050:
6048:
6043:
6042:
6037:
6034:
6032:
6028:
6027:Coxeter group
6011:
6001:
5989:
5980:
5979:
5946:
5913:
5880:
5847:
5814:
5781:
5748:
5745:
5716:
5713:
5710:
5701:
5700:
5697:
5664:
5632:
5629:
5571:
5566:
5563:
5554:
5553:
5550:
5517:
5484:
5451:
5419:
5416:
5348:
5344:
5341:
5332:
5331:
5327:
5324:
5319:
5317:
5312:
5310:
5307:
5305:
5300:
5299:
5294:
5291:
5289:
5288:Coxeter group
5252:
5251:
5228:
5205:
5182:
5179:
5160:
5157:
5154:
5145:
5144:
5140:
5118:
5115:
5077:
5072:
5069:
5060:
5059:
5055:
5033:
5030:
5011:
5008:
5005:
4996:
4995:
4992:
4949:
4906:
4863:
4821:
4818:
4750:
4746:
4743:
4734:
4733:
4730:
4687:
4643:
4600:
4557:
4514:
4472:
4469:
4430:
4428:
4425:
4416:
4415:
4411:
4408:
4403:
4401:
4396:
4394:
4391:
4389:
4384:
4383:
4378:
4375:
4373:
4369:
4368:Coxeter group
4321:
4319:
4312:
4307:
4306:
4301:
4296:
4294:
4287:
4283:
4269:
4264:
4260:
4258:
4253:
4249:
4247:
4242:
4238:
4236:
4231:
4227:
4225:
4220:
4216:
4214:
4209:
4205:
4203:
4198:
4194:
4189:
4188:
4185:
4180:
4176:
4174:
4169:
4165:
4163:
4158:
4154:
4152:
4147:
4143:
4141:
4136:
4132:
4130:
4125:
4121:
4119:
4114:
4110:
4107:
4106:
4102:
4098:
4095:
4091:
4088:
4084:
4081:
4077:
4074:
4070:
4067:
4063:
4060:
4056:
4053:
4052:
4049:
4045:
4043:
4040:
4038:
4035:
4033:
4030:
4028:
4025:
4023:
4020:
4018:
4015:
4012:
4011:
4004:
4001:
3998:
3995:
3992:
3991:
3988:
3982:
3980:
3977:
3974:
3973:
3968:
3910:
3905:
3901:
3848:
3843:
3839:
3809:
3804:
3800:
3752:
3747:
3743:
3713:
3708:
3704:
3656:
3651:
3647:
3617:
3612:
3608:
3578:
3573:
3572:
3568:
3564:
3561:
3557:
3554:
3550:
3547:
3543:
3540:
3536:
3533:
3529:
3526:
3522:
3519:
3518:
3444:
3443:{4,3,∞}
3440:
3367:
3364:
3324:
3321:
3215:
3212:
3172:
3169:
3058:
3055:
3015:
3012:
2971:
2970:
2963:
2960:
2957:
2954:
2951:
2950:
2947:
2942:
2939:
2937:
2934:
2931:
2930:
2925:
2922:
2920:
2917:
2913:
2876:
2871:
2867:
2837:
2832:
2828:
2798:
2793:
2789:
2759:
2754:
2750:
2720:
2715:
2711:
2681:
2676:
2672:
2642:
2637:
2633:
2630:
2629:
2625:
2621:
2618:
2614:
2611:
2607:
2604:
2600:
2597:
2593:
2590:
2586:
2583:
2579:
2576:
2575:
2420:
2419:{∞,3,4}
2416:
2262:
2259:
2191:
2188:
2044:
2041:
1973:
1970:
1816:
1813:
1745:
1742:
1739:
1738:
1731:
1728:
1725:
1722:
1719:
1718:
1715:
1710:
1707:
1705:
1702:
1699:
1698:
1693:
1690:
1688:
1685:
1680:
1678:
1674:
1670:
1666:
1662:
1659:
1644:
1640:
1637:
1633:
1630:
1626:
1623:
1622:
1618:
1614:
1611:
1607:
1604:
1600:
1597:
1596:
1589:
1586:
1583:
1582:
1576:
1574:
1573:square tiling
1570:
1566:
1552:8: abcd/efgh
1551:
1548:
1544:
1541:
1459:
1456:
1452:4: abcd/abcd
1451:
1448:
1444:
1441:
1397:
1395:
1391:2: abba/abba
1390:
1387:
1383:
1376:
1327:
1325:
1321:2: aaaa/bbbb
1320:
1317:
1313:
1310:
1217:
1215:
1211:4: abbb/bbba
1210:
1208:
1201:
1182:
1173:
1169:4: abbc/bccd
1168:
1165:
1161:
1154:
1115:
1107:
1103:2: abba/baab
1102:
1099:
1095:
1092:
1025:
1016:
1012:1: aaaa/aaaa
1011:
1008:
1004:
1001:
881:
873:
868:
863:
861:
858:
856:
853:
851:
847:
844:
843:
840:
838:
787:
784:
735:
676:
673:
671:
668:
661:
658:
649:
636:
633:
631:
628:
617:
612:
607:
602:
597:
593:
590:
585:
581:
578:
574:
571:
567:
564:
560:
557:
553:
550:
541:
534:
527:
520:
513:
507:
504:
500:
497:
495:
494:trapezohedron
490:
488:
484:
482:
478:
476:
473:
471:
468:
464:
461:
459:
456:
454:
451:
449:
446:
444:
440:
437:
435:
432:
431:
428:
420:
418:
414:
409:
407:
406:square tiling
403:
399:
389:
387:
383:
379:
375:
371:
367:
362:
360:
359:
354:
350:
346:
342:
341:space-filling
338:
333:
331:
327:
323:
319:
315:
312:is a regular
311:
310:vertex figure
307:
303:
299:
295:
291:
287:
278:
274:
271:
267:
263:
257:
254:
252:
248:
230:
220:
209:
207:
206:Coxeter group
203:
193:
191:
187:
183:
180:
175:
171:
169:
168:Vertex figure
165:
161:
158:
154:
150:
146:
143:
139:
99:
97:
93:
89:
87:
83:
63:
59:
56:
53:
49:
46:
43:
39:
35:
30:
25:
20:
18530:
18518:
18506:
18486:
18083:
17655:
17643:
17627:
17612:
17608:
17591:
17574:
17552:
17543:
17528:
17519:
17468:
17387:
17385:
17157:
17150:
17143:
17123:tessellation
17118:
17114:
17112:
16926:sr{4,4}×{∞}
16887:
16880:
16873:
16853:tessellation
16848:
16844:
16842:
16609:
16594:
16545:
16543:
16352:
16341:
16322:
16273:
16269:
16267:
16003:
15987:
15978:
15976:
15763:
15759:
15757:
15564:
15545:
15534:
15523:
15511:
15493:
15437:
15188:
15126:pmm (*2222)
15105:
15103:
15075:b-tCO-trille
15074:
15069:
15046:tessellation
15041:
15037:
15035:
14776:
14765:
14749:
14731:
14714:
14632:
14631:is called a
14628:
14626:
14596:
14534:pmm (*2222)
14513:
14511:
14464:1-RCO-trille
14463:
14458:
14405:
14366:
14362:
14360:
14088:
14077:
14065:
14051:
14038:
14027:
14016:
13955:
13953:
13668:
13585:
13573:
13569:
13567:
13268:
13257:
13241:
13223:
13184:
13167:
13084:
13083:is called a
13080:
13078:
12796:
12734:pmm (*2222)
12713:
12711:
12694:
12666:n-tCO-trille
12665:
12660:
12633:tessellation
12628:
12624:
12622:
12289:
12239:
12238:is called a
12235:
12233:
12203:cuboctahedra
12188:
11916:
11854:pmm (*2222)
11833:
11831:
11773:2-RCO-trille
11772:
11767:
11752:cuboctahedra
11740:tessellation
11735:
11731:
11729:
11178:
11074:
11070:
11068:
10641:
10627:
10615:
10605:
9691:
9601:pmm (*2222)
9568:
9566:
9540:
9532:
9527:
9476:tessellation
9469:
9179:
9168:
9157:
8867:
8805:pmm (*2222)
8784:
8782:
8765:
8756:
8751:
8728:tessellation
8723:
8719:
8717:
8402:
8387:
8307:
7704:
7642:pmm (*2222)
7621:
7619:
7602:
7593:
7588:
7581:square prism
7577:cuboctahedra
7565:tessellation
7560:
7556:
7554:
7452:square prism
5985:
5777:
5749:
5257:
5201:
5183:
5116:Quarter × 2
4510:
4327:
4314:
4308:
4297:
4289:
4279:
4021:
4005:Paracompact
3983:Euclidean E
3056:
2964:Paracompact
2909:
1732:Paracompact
1681:
1668:
1655:
1593:pmm (*2222)
1564:
1562:
834:
608:P4/mmm (123)
479:Rectangular
458:Rhombohedral
448:Orthorhombic
426:
410:
395:
386:circumsphere
363:
358:tessellation
356:
352:
348:
340:
334:
329:
294:tessellation
289:
285:
283:
17652:A. Andreini
17392:alternation
16615:symmetry).
16328:symmetry),
16008:Cell views
15940:tetrahedron
15830:tetrahedral
15768:alternation
15294:Space group
15123:p4m (*442)
15120:p6m (*632)
15100:Projections
14531:p4m (*442)
14528:p6m (*632)
14508:Projections
14314:Space group
14022:symmetry),
13591:symmetry),
12908:Space group
12731:p4m (*442)
12728:p6m (*632)
12708:Projections
12031:Space group
11851:p4m (*442)
11848:p6m (*632)
11828:Projections
11638:Space group
11193:Space group
10621:-symmetric
9761:Space group
9598:p4m (*442)
9595:p6m (*632)
9563:Projections
9555:cells with
9549:tetrahedron
9492:bitruncated
9486:made up of
9324:Edge figure
8979:Space group
8802:p4m (*442)
8799:p6m (*632)
8779:Projections
8761:pyramidille
8694:Pyramidille
8626:Space group
8370:symmetry .
7890:Space group
7639:p4m (*442)
7636:p6m (*632)
7616:Projections
7459:Space group
5569:↔ <>
5328:Honeycombs
4412:Honeycombs
4268:{3,∞}
4184:{∞,3}
4008:Noncompact
3909:{3,∞}
2967:Noncompact
2875:{∞,3}
1735:Noncompact
1590:p4m (*442)
1587:p6m (*632)
1559:Projections
850:Space group
624:P432 (207)
592:Space group
506:Point group
304:made up of
186:Space group
18567:Categories
17511:References
17456:tetrahedra
17374:Properties
17102:Properties
16924:s{4,4}×{∞}
16832:Properties
16532:Properties
16330:snub cubes
16256:Properties
15966:Properties
15814:snub cubes
15746:Properties
15560:tetrahedra
15548:snub cubes
15025:Properties
14757:tetrahedra
14350:Properties
14054:icosahedra
14024:icosahedra
13964:rectangles
13942:Properties
13593:tetrahedra
13582:icosahedra
13578:snub cubes
13556:Properties
13253:octahedron
13249:tetrahedra
13197:Two views
13165:symmetry.
12864:=<>
12612:Properties
12215:tetrahedra
11987:=<>
11719:Properties
11225:F23 (196)
11057:Properties
10653:rectangles
10638:tetrahedra
10558:Colored by
10551:(order 2)
10547:(order 1)
10543:(order 2)
10539:(order 4)
10535:(order 8)
9704:) for the
9446:Properties
9164:tetrahedra
8973:=<>
8707:Properties
8617:isosceles
7540:Properties
4311:tetrahedra
1684:octahedral
1658:4-polytope
866:honeycomb
610:P422 (89)
605:P222 (16)
453:Tetragonal
439:Monoclinic
376:, such as
345:polyhedral
316:. It is a
314:octahedron
269:Properties
179:octahedron
18491:honeycomb
18485:Uniform (
18062:Hexagonal
17995:−
17985:~
17949:~
17913:~
17880:−
17870:~
17837:−
17827:~
17794:−
17784:~
17751:−
17741:~
17573:, (2008)
17450:from the
17198:{4,4,2,∞}
17127:honeycomb
16857:honeycomb
16651:{4,4,2,∞}
16608:but with
16589:. It has
16340:but with
16317:. It has
15824:from the
15816:from the
15556:octahedra
15542:Dual cell
15327:Coloring
15315:Fibrifold
15267:~
15229:~
15117:Symmetry
15050:honeycomb
14983:~
14784:Dual cell
14738:octahedra
14691:~
14525:Symmetry
14375:honeycomb
14288:~
14096:Dual cell
14058:octahedra
14011:. It has
13966:from the
13309:sr{4,3,4}
13276:Dual cell
13144:~
13060:symmetry
12941:Coloring
12929:Fibrifold
12882:~
12842:~
12725:Symmetry
12637:honeycomb
12550:~
12211:octahedra
12195:octahedra
12170:symmetry
12126:Coloring
12005:~
11965:~
11845:Symmetry
11744:honeycomb
11677:~
11231:Fibrifold
11015:~
10695:2s{4,3,4}
10649:pentagons
10634:octahedra
10531:symmetry
10201:~
10133:~
10060:=<>
10037:~
9941:~
9843:~
9803:Fibrifold
9719:~
9592:Symmetry
9480:honeycomb
9401:~
9235:2t{4,3,4}
9187:Dual cell
9160:octahedra
8999:Coloring
8951:~
8913:~
8796:Symmetry
8740:octahedra
8732:honeycomb
8664:~
8590:Face type
8566:Cell type
8410:Dual cell
8390:octahedra
8269:order 16
8258:symmetry
7932:Coloring
7864:~
7825:~
7786:~
7747:~
7633:Symmetry
7573:octahedra
7569:honeycomb
7497:~
7004:~
6966:~
6884:~
6846:~
6709:~
6668:~
6581:<2>
6507:~
6316:~
6275:~
6150:~
6052:Fibrifold
6005:~
5714:<>
5309:Fibrifold
5031:Half × 2
4393:Fibrifold
4305:Dual cell
1661:tesseract
1584:Symmetry
615:R3 (146)
613:R3m (160)
603:Pmmm (47)
470:Unit cell
443:Triclinic
366:Euclidean
324:{4,3,4}.
318:self-dual
298:honeycomb
256:self-dual
224:~
156:Face type
141:Cell type
61:Indexing
17473:See also
17366:Symmetry
17341:triangle
17204:{4,4,∞}
17063:triangle
16657:{4,4,∞}
16477:triangle
16394:{4,3,4}
16210:triangle
16109:{4,3,4}
15947:Symmetry
15865:{4,3,4}
15727:Symmetry
15697:triangle
15609:{4,3,4}
15309:m (229)
15211:Symmetry
15185:Symmetry
14821:{4,3,4}
14230:triangle
14133:{4,3,4}
13894:triangle
13802:{4,3,4}
13465:triangle
13311:sr{4,3}
13068:order 1
13064:order 2
12923:m (225)
12793:Symmetry
12336:tr{4,3}
12178:order 1
12174:order 2
11913:Symmetry
11471:rr{4,3}
11430:quarter
10976:triangle
9797:m (227)
9790:3m (216)
9688:Symmetry
9509:, it is
9241:{4,3,4}
8864:Symmetry
8594:triangle
8302:order 4
8291:order 8
8280:order 8
7728:Symmetry
7701:Symmetry
7428:triangle
6198:<>
6075:Extended
6072:diagram
6070:Extended
6066:symmetry
6064:Extended
6059:symmetry
5567:<>
5322:diagram
5320:Extended
5316:symmetry
5314:Extended
4406:diagram
4404:Extended
4400:symmetry
4398:Extended
4372:expanded
4002:Compact
2961:Compact
1729:Compact
1206:{4,3,4}
1180:m (229)
1159:{4,3,4}
1113:m (221)
1023:m (225)
1002:{4,3,4}
879:m (221)
551:Diagram
546:, (432)
544:Order 48
542:, (*432)
532:, (422)
530:Order 16
528:, (*422)
525:, (222)
521:, (*222)
491:Trigonal
90:{4,3,4}
18528:qδ
18516:hδ
18471:qδ
18463:hδ
18432:qδ
18424:hδ
18371:qδ
18362:hδ
18310:qδ
18300:hδ
18255:qδ
18245:hδ
18206:qδ
18196:hδ
18154:qδ
18144:hδ
18105:qδ
18095:hδ
18053:qδ
18043:hδ
17707:regular
17536:A000029
17202:0,1,2,3
16799:octagon
16655:0,1,2,3
15863:0,1,2,3
15607:0,1,2,3
15461:4.8.4.8
15452:4.4.4.6
15302:m (221)
14953:m (229)
14910:octagon
14905:hexagon
14876:tr{4,3}
14819:0,1,2,3
14635:, with
14454:regular
14398:pyramid
14326:m (221)
14262:pyramid
14240:octagon
14188:rr{4,3}
13087:, with
12916:m (221)
12602:Cells:
12588:m (221)
12500:octagon
12495:hexagon
12457:tr{4,3}
12334:{4,3,4}
12221:with a
11650:m (221)
11592:rr{4,3}
11469:{4,3,4}
11427:double
11425:quarter
11416:double
10697:2s{4,3}
10441:1:1:1:1
9783:m (225)
9776:m (221)
9769:m (229)
9559:faces.
9535:in his
9372:m (229)
9316:hexagon
8638:m (221)
8599:octagon
8449:t{4,3}
8447:{4,3,4}
8320:. This
8314:hexagon
7968:diagram
7966:Coxeter
7721:below.
7471:m (221)
7093:2r{4,3}
7089:{4,3,4}
6173:(None)
4192:figure
4042:{8,3,8}
4037:{7,3,7}
4032:{6,3,6}
4027:{5,3,5}
4022:{4,3,4}
4017:{3,3,3}
3999:Affine
3996:Finite
3366:{4,3,8}
3323:{4,3,7}
3214:{4,3,6}
3171:{4,3,5}
3057:{4,3,4}
3014:{4,3,3}
2958:Affine
2955:Finite
2261:{8,3,4}
2190:{7,3,4}
2043:{6,3,4}
1972:{5,3,4}
1815:{4,3,4}
1744:{3,3,4}
1726:Affine
1723:Finite
864:Partial
622:m (221)
600:P1 (1)
539:, (33)
537:Order 6
535:, (*33)
523:Order 8
516:Order 2
485:Square
419:cells.
400:, with
330:cubille
277:regular
198:m (221)
18504:δ
18455:δ
18416:δ
18352:δ
18290:δ
18235:δ
18186:δ
18134:δ
18085:δ
18033:δ
17723:Family
17719:Space
17634:
17600:
17581:
17346:square
17317:s{2,4}
17092:Cell:
17068:square
17048:{}x{3}
17039:{}x{4}
16822:Cell:
16794:square
16779:{}x{4}
16770:{}x{8}
16593:(with
16522:Cell:
16482:square
16462:{}x{4}
16321:(with
16246:Cell:
16215:square
16195:{}x{3}
16186:{}x{4}
16177:s{4,3}
15702:square
15673:s{2,4}
15664:s{4,3}
15288:×2, ]
15157:Frame
15131:Solid
15090:
14900:square
14885:{}x{8}
14748:(both
14565:Frame
14539:Solid
14389:, and
14235:square
14215:{}x{4}
14206:{}x{8}
14197:t{4,3}
14026:(with
14015:(with
13932:Cell:
13899:square
13879:{}x{3}
13870:s{3,3}
13584:(with
13546:Cell:
13470:square
13441:s{3,3}
13432:s{4,3}
13058:figure
13056:Vertex
12765:Frame
12739:Solid
12691:Images
12681:
12647:, and
12490:square
12475:{}x{4}
12466:t{3,4}
12168:figure
12166:Vertex
11885:Frame
11859:Solid
11797:Images
11754:, and
11709:Cell:
11610:{}x{4}
11601:r{4,3}
11413:Order
11148:, and
11047:Cell:
10961:s{3,3}
10699:sr{3}
10529:figure
10527:Vertex
10156:
9646:Frame
9606:Solid
9436:Cell:
9311:square
9296:t{3,4}
9210:
8836:Frame
8810:Solid
8697:Cell:
8570:t{4,3}
8278:(*222)
8267:(*224)
8256:figure
8254:Vertex
7927:(216)
7713:, and
7673:Frame
7647:Solid
7530:Cell:
7433:square
7404:r{4,3}
7091:r{4,3}
7045:
6941:(229)
6925:
6774:(204)
6759:
6567:(221)
6551:
6416:(227)
6400:
6366:
6184:(225)
6091:(216)
6077:group
6057:Square
5708:(221)
5561:(225)
5339:(225)
5325:Order
5258:The ,
5152:(229)
5067:(227)
5003:(217)
4741:(225)
4423:(221)
4409:Order
4328:The ,
4190:Vertex
4108:Cells
4054:Image
3975:Space
3577:figure
3575:Vertex
3520:Image
2932:Space
2631:Cells
2577:Image
1700:Space
1624:Frame
1598:Solid
1093:{4,3}
598:Pm (6)
518:, (1)
487:cuboid
481:cuboid
415:using
353:tiling
259:Cell:
160:square
51:Family
17505:Voxel
17460:cubes
17337:Faces
17326:{3,3}
17313:Cells
17196:1,2,3
17135:cubes
17129:) in
17059:Faces
17035:Cells
16869:cubes
16859:) in
16790:Faces
16766:Cells
16649:0,1,3
16602:cubes
16473:Faces
16453:{3,4}
16445:Cells
16334:cubes
16206:Faces
16168:{3,4}
16160:Cells
15693:Faces
15682:{3,3}
15660:Cells
15508:cubes
15015:Cell
14896:Faces
14872:Cells
14742:cubes
14391:cubes
14340:Cell
14226:Faces
14184:Cells
14131:0,1,3
13968:cubes
13890:Faces
13861:{3,4}
13853:Cells
13461:Faces
13450:{3,3}
13428:Cells
13234:cubes
13189:with
12649:cubes
12486:Faces
12453:Cells
12332:0,1,2
12246:with
11760:wedge
11756:cubes
11631:wedge
11588:Cells
11422:half
11419:full
11222:(203)
11215:(202)
11208:(200)
11201:(204)
10972:Faces
10952:{3,3}
10948:Cells
10560:cell
10556:Image
10420:2:1:1
9482:) in
9307:Faces
9292:Cells
8579:{3,4}
8300:(*22)
8289:(*44)
7918:(225)
7909:(225)
7900:(221)
7424:Faces
7413:{3,4}
7400:Cells
7095:r{3}
6432:or ]
6047:group
6045:Space
5304:group
5302:Space
4819:Half
4388:group
4386:Space
4286:cubes
4282:cubes
4257:{3,8}
4246:{3,7}
4235:{3,6}
4224:{3,5}
4213:{3,4}
4202:{3,3}
4173:{8,3}
4162:{7,3}
4151:{6,3}
4140:{5,3}
4129:{4,3}
4118:{3,3}
4013:Name
3993:Form
3847:{3,8}
3808:{3,7}
3751:{3,6}
3712:{3,5}
3655:{3,4}
3616:{3,3}
2952:Form
2919:cells
2916:cubic
2836:{8,3}
2797:{7,3}
2758:{6,3}
2719:{5,3}
2680:{4,3}
2641:{3,3}
1740:Name
1720:Form
514:, (*)
509:Order
463:Cubic
349:cells
339:is a
306:cubic
300:) in
145:{4,3}
66:11,15
18489:-1)-
17709:and
17632:ISBN
17598:ISBN
17579:ISBN
17348:{4}
17179:Type
17137:and
17125:(or
17113:The
17085:Dual
17070:{4}
16909:Type
16867:and
16855:(or
16843:The
16815:Dual
16801:{8}
16632:Type
16606:cube
16544:The
16519:Dual
16484:{4}
16375:Type
16351:(as
16338:cube
16268:The
16243:Dual
16217:{4}
16090:Type
16019:Net
15956:Dual
15916:Cell
15848:Type
15736:Dual
15704:{4}
15590:Type
15322:8:2
15197:and
15104:The
15056:and
15048:(or
15036:The
15008:Dual
14912:{8}
14802:Type
14512:The
14373:(or
14361:The
14333:Dual
14328:4:2
14242:{8}
14114:Type
14064:(as
14037:(as
13954:The
13929:Dual
13901:{4}
13783:Type
13568:The
13505:Dual
13472:{4}
13294:Type
13240:(as
12936:2:2
12712:The
12635:(or
12623:The
12595:Dual
12590:4:2
12502:{8}
12315:Type
12242:, a
12219:cube
11832:The
11742:(or
11730:The
11702:Dual
11652:4:2
11450:Type
11069:The
11040:Dual
10978:{3}
10680:Type
10655:, 4
10651:, 4
10610:and
9819:2:2
9747:and
9567:The
9478:(or
9470:The
9427:Dual
9331:{3}
9318:{6}
9220:Type
8783:The
8738:and
8730:(or
8718:The
8690:Dual
8640:4:2
8601:{8}
8428:Type
7620:The
7575:and
7567:(or
7555:The
7523:Dual
7473:4:2
7435:{4}
7070:Type
6949:↔ ]
6944:8:2
6790:↔ ]
6570:4:2
6419:2:2
6187:2:2
6094:1:2
5711:4:2
5564:2:2
5342:2:2
5229:,
5155:8:2
5075:↔ ]
5070:2:2
5006:4:2
4744:2:2
4426:4:2
3441:...
2972:Name
2417:...
1563:The
499:Cube
296:(or
284:The
251:Dual
200:4:2
162:{4}
41:Type
17343:{3}
17117:or
17065:{3}
16847:or
16796:{4}
16479:{3}
16392:0,3
16272:or
16212:{3}
15861:dht
15762:or
15758:An
15699:{3}
15319:4:2
15250:,
15040:or
14956:8:2
14907:{6}
14902:{4}
14365:or
14237:{4}
14232:{3}
13896:{3}
13628:or
13572:or
13467:{3}
12933:4:2
12627:or
12497:{6}
12492:{4}
11734:or
11467:0,2
11073:or
11000:],
10468:1:1
10405:1:1
9816:1:2
9813:2:2
9810:4:2
9807:8:2
9583:.
9422:,
9375:8:2
9313:{4}
9239:1,2
8722:or
8685:,
8596:{3}
8445:0,1
7559:or
7518:,
7430:{3}
7025:×2
6928:(*)
6905:×2
6869:↔ ½
6780:r8
6583:↔
6573:d4
6422:g2
6200:↔
6190:d2
6097:a1
6033::
5878:(6)
5746:×2
5695:(3)
5662:(1)
5630:×2
5417:×1
5346:↔
5206:,
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