13495:
15578:
13560:
14510:
17369:
13215:
11061:
15485:
13222:
12712:
13500:
16238:
13060:
12530:
10517:
14779:
13271:
9149:
15537:
14091:
10999:
8251:
13689:
17106:
16507:
16260:
14790:
13282:
8244:
15548:
14102:
9690:
9683:
9669:
9662:
9182:
9676:
13924:
10531:
15725:
10524:
16536:
12170:
16887:
4311:
9193:
4112:
4105:
4098:
3578:
3571:
3564:
2635:
2628:
2621:
14265:
13946:
13053:
12525:
4230:
15932:
9650:
9643:
9629:
9622:
9636:
14935:
1458:
1397:
14595:
14588:
14581:
12795:
12788:
12781:
12964:
10503:
9354:
15187:
15180:
15173:
14569:
14562:
14555:
12769:
12762:
12755:
12307:
12957:
11723:
11637:
10510:
8258:
17157:
15161:
15154:
15147:
14732:
13734:
8416:
15476:
14354:
15350:
15343:
11915:
11908:
11901:
10604:
10576:
9156:
8624:
8237:
7458:
3718:
11889:
11882:
11875:
10583:
2593:
10597:
10590:
13185:
12149:
8866:
8859:
8852:
7703:
7696:
7689:
6436:
4070:
3536:
12616:
14489:
12689:
12142:
11817:
8840:
8833:
8826:
7677:
7670:
7663:
4252:
3814:
15436:
10441:
10435:
10426:
10420:
10411:
9015:
6794:
6111:
16192:
15679:
13885:
13456:
13447:
10976:
7969:
7962:
7955:
15429:
1327:
1175:
14891:
12472:
10489:
10483:
10474:
10468:
10462:
10456:
10447:
9022:
6587:
8387:
15730:
9450:
7948:
16468:
16183:
14212:
14203:
13876:
12481:
11607:
9311:
8585:
11796:
9218:
12163:
15029:
17341:
15697:
13465:
11616:
10967:
8594:
7428:
7419:
160:
45:
1558:
1109:
1018:
7544:
185:
4241:
4219:
4157:
3757:
3661:
2764:
16009:
14622:
14627:
15492:
1647:
1640:
1654:
8711:
1621:
1614:
15098:
1628:
4168:
2803:
4091:
2614:
16079:
16065:
16042:
16072:
16058:
16049:
16836:
273:
4084:
3557:
3550:
2607:
8779:
7616:
17332:
17063:
17054:
16794:
16477:
16210:
16201:
15688:
14230:
13894:
12490:
11625:
6204:
14496:
40:
4274:
4263:
3915:
3853:
4077:
3543:
2600:
16785:
14900:
14221:
16026:
574:
588:
4190:
4179:
2881:
2842:
4208:
3622:
567:
4146:
581:
2725:
12695:
11801:
4124:
2647:
16035:
11824:
4135:
2686:
15104:
8784:
7621:
595:
9224:
15467:
14503:
11088:
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
9474:
15457:. 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.
13680:
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.
13179:
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.
15505:
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
13204:
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.
17099:
15212:. 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.
16829:
18021:
17906:
17863:
17820:
17777:
6397:
6363:
10182:
10114:
10076:
10028:
10018:
6266:
6227:
17979:
17943:
15297:
15259:
15013:
14721:
14318:
13174:
12912:
12872:
12580:
12035:
11995:
11707:
11045:
10231:
10163:
10067:
9971:
9873:
9749:
9431:
8981:
8943:
8694:
7894:
7855:
7816:
7777:
7527:
7034:
6996:
6914:
6876:
6739:
6698:
6537:
6346:
6305:
6180:
6035:
5553:
5520:
5487:
5454:
5383:
5143:
5102:
4804:
3969:
3523:
3170:
3155:
3140:
2570:
2527:
1971:
1956:
1941:
1928:
1913:
1898:
1504:
1489:
1474:
1442:
1427:
1412:
1311:
1296:
1281:
964:
949:
934:
254:
15404:
11387:
11377:
11290:
10617:
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
10394:
10384:
10268:
10252:
10242:
9932:
9922:
7052:
7042:
6932:
6922:
6826:
6817:
6807:
6610:
6548:
6449:
5751:
5625:
5606:
5244:
5221:
5185:
5175:
5111:
3175:
3160:
3145:
2565:
2560:
2522:
2517:
2407:
2402:
2364:
2359:
2184:
2146:
1976:
1961:
1946:
1933:
1918:
1903:
1509:
1494:
1479:
1447:
1432:
1417:
1316:
1301:
1286:
969:
954:
939:
15414:
13635:
13393:
13038:
12418:
12129:
11553:
11406:
11368:
11173:
11155:
10903:
10827:
10781:
10365:
10326:
8173:
7365:
7243:
6756:
5982:
5949:
5916:
5883:
5700:
5254:
5208:
5058:
5036:
3327:
2580:
2422:
2194:
1207:
15919:
15909:
15899:
15889:
14683:
14663:
14653:
13761:
13751:
13741:
13542:
13532:
13522:
13431:
13126:
13116:
13106:
12456:
12284:
12264:
11591:
10951:
10921:
10855:
10819:
10192:
10172:
10124:
10104:
10086:
10000:
9990:
9904:
9894:
9095:
8569:
8133:
8103:
8064:
8055:
7403:
7373:
7345:
7317:
7281:
7215:
6649:
6639:
6620:
6600:
6498:
6468:
6256:
6237:
6217:
5741:
5731:
5680:
5647:
5586:
5422:
5402:
5392:
5373:
5363:
4965:
4922:
4879:
4836:
4824:
4814:
4795:
4785:
4765:
4475:
4465:
4455:
4445:
1098:
17443:
17433:
17423:
17306:
17296:
17286:
17276:
17258:
17248:
17238:
17028:
17018:
17008:
16998:
16980:
16960:
16950:
16759:
16749:
16739:
16729:
16711:
16691:
16681:
16596:
16586:
16576:
16566:
16448:
16438:
16428:
16418:
16324:
16314:
16304:
16294:
16163:
16153:
16143:
16133:
15819:
15809:
15799:
15789:
15663:
15653:
15643:
15633:
15395:
15385:
15375:
15365:
14875:
14865:
14855:
14845:
14455:
14435:
14425:
14187:
14167:
14157:
14008:
13998:
13988:
13846:
13836:
13826:
13716:
13706:
13696:
13663:
13653:
13643:
13630:
13625:
13615:
13421:
13411:
13401:
13388:
13383:
13373:
13355:
13345:
13335:
13033:
13028:
13018:
12999:
12989:
12979:
12446:
12436:
12426:
12413:
12408:
12398:
12380:
12370:
12360:
12124:
12109:
12090:
12070:
11581:
11561:
11548:
11533:
11515:
11495:
11416:
11411:
11401:
11396:
11363:
11358:
11329:
11319:
11183:
11178:
11168:
11163:
11150:
11145:
11117:
11107:
10941:
10931:
10913:
10908:
10898:
10893:
10875:
10865:
10837:
10832:
10809:
10799:
10776:
10771:
10743:
10733:
10375:
10370:
10360:
10355:
10336:
10331:
10307:
10297:
10187:
10177:
10119:
10109:
10081:
9285:
9275:
9114:
9104:
9075:
9065:
9052:
9047:
9037:
8549:
8539:
8526:
8521:
8511:
8483:
8473:
8369:
8349:
8339:
8222:
8217:
8207:
8202:
8178:
8159:
8154:
8113:
8074:
8035:
7996:
7383:
7360:
7332:
7327:
7309:
7304:
7294:
7289:
7271:
7238:
7195:
7172:
7167:
7129:
6761:
6751:
6615:
6605:
6558:
6459:
6407:
6402:
6392:
6387:
6368:
6358:
6261:
6232:
6222:
6136:
6126:
5977:
5972:
5962:
5944:
5939:
5911:
5896:
5878:
5845:
5840:
5830:
5812:
5807:
5779:
5764:
5746:
5695:
5662:
5630:
5620:
5615:
5601:
5548:
5543:
5533:
5515:
5510:
5482:
5467:
5449:
5378:
5288:
5198:
5133:
5121:
5092:
5048:
5026:
4995:
4985:
4952:
4899:
4809:
4733:
4713:
4703:
4680:
4670:
4660:
4636:
4616:
4583:
4573:
4540:
4487:
3964:
3959:
3954:
3926:
3907:
3902:
3897:
3892:
3864:
3825:
3806:
3801:
3796:
3768:
3729:
3705:
3700:
3672:
3633:
3594:
3518:
3513:
3498:
3460:
3446:
3441:
3436:
3421:
3383:
3340:
3317:
3312:
3297:
3289:
3284:
3269:
3231:
3188:
3127:
3112:
3074:
3031:
2988:
2892:
2853:
2814:
2775:
2736:
2697:
2658:
2555:
2545:
2512:
2489:
2474:
2436:
2412:
2397:
2387:
2369:
2354:
2331:
2316:
2278:
2260:
2245:
2207:
2179:
2174:
2164:
2141:
2136:
2113:
2098:
2060:
2042:
2027:
1989:
1885:
1870:
1832:
1814:
1799:
1761:
1547:
1537:
1527:
1517:
1372:
1352:
1272:
1262:
1232:
1197:
1160:
1130:
1068:
1055:
1040:
997:
987:
977:
896:
802:
780:
750:
731:
711:
691:
114:
17448:
17311:
17263:
17033:
16985:
16764:
16716:
11300:
10278:
9057:
8531:
8212:
8164:
7337:
7299:
7177:
6836:
6131:
5850:
5817:
5784:
5667:
5293:
5231:
3941:
3710:
3485:
3302:
3132:
2897:
2550:
2537:
2507:
2494:
2479:
2441:
2392:
2379:
2349:
2336:
2265:
2169:
2156:
2131:
2118:
2047:
1890:
1819:
1377:
1267:
1060:
785:
736:
716:
696:
17534:
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).
17453:
17413:
17316:
17268:
17228:
17038:
16990:
16970:
16769:
16721:
16701:
15409:
14673:
14445:
14177:
14018:
13856:
13771:
13726:
13673:
13552:
13365:
13136:
13009:
12390:
12294:
12274:
12119:
12100:
12080:
11571:
11543:
11525:
11505:
11348:
11339:
11309:
11295:
11135:
11127:
11097:
10885:
10847:
10789:
10761:
10753:
10723:
10346:
10317:
10287:
10273:
10096:
10010:
9980:
9914:
9884:
9295:
9265:
9134:
9124:
9085:
8559:
8503:
8493:
8359:
8193:
8183:
8144:
8123:
8094:
8084:
8045:
8025:
8016:
8006:
7986:
7393:
7355:
7261:
7251:
7233:
7223:
7205:
7185:
7157:
7149:
7139:
7119:
6831:
6766:
6746:
6659:
6629:
6488:
6478:
6373:
6353:
6246:
6141:
6121:
5929:
5906:
5873:
5863:
5797:
5774:
5690:
5657:
5635:
5596:
5500:
5477:
5444:
5434:
5412:
5283:
5273:
5249:
5226:
5203:
5180:
5138:
5097:
5053:
5031:
4975:
4942:
4932:
4909:
4889:
4866:
4856:
4846:
4775:
4723:
4690:
4646:
4626:
4603:
4593:
4560:
4550:
4530:
4517:
4507:
4497:
4373:
4363:
4353:
4343:
3946:
3936:
3884:
3874:
3845:
3835:
3788:
3778:
3749:
3739:
3692:
3682:
3653:
3643:
3614:
3604:
3508:
3490:
3480:
3470:
3431:
3413:
3403:
3393:
3370:
3360:
3350:
3322:
3307:
3279:
3261:
3251:
3241:
3218:
3208:
3198:
3122:
3104:
3094:
3084:
3061:
3051:
3041:
3018:
3008:
2998:
2912:
2902:
2873:
2863:
2834:
2824:
2795:
2785:
2756:
2746:
2717:
2707:
2678:
2668:
2575:
2532:
2502:
2484:
2466:
2456:
2446:
2417:
2374:
2344:
2326:
2308:
2298:
2288:
2255:
2237:
2227:
2217:
2189:
2151:
2126:
2108:
2090:
2080:
2070:
2037:
2019:
2009:
1999:
1880:
1862:
1852:
1842:
1809:
1791:
1781:
1771:
1382:
1362:
1342:
1252:
1242:
1202:
1150:
1140:
1088:
1078:
1050:
1007:
926:
916:
906:
832:
822:
812:
790:
770:
760:
741:
721:
701:
144:
134:
124:
11382:
10389:
10247:
10023:
9927:
7047:
6927:
6812:
6553:
6454:
5116:
1532:
992:
17438:
17301:
17253:
8344:
1542:
17428:
17418:
17291:
17281:
17243:
17233:
17023:
17013:
17003:
16975:
16965:
16955:
16754:
16744:
16734:
16706:
16696:
16686:
16591:
16581:
16571:
16443:
16433:
16423:
16319:
16309:
16299:
16158:
16148:
16138:
15914:
15904:
15894:
15814:
15804:
15794:
15658:
15648:
15638:
15390:
15380:
15370:
14870:
14860:
14850:
14678:
14668:
14658:
14450:
14440:
14430:
14182:
14172:
14162:
14013:
14003:
13993:
13851:
13841:
13831:
13766:
13756:
13746:
13721:
13711:
13701:
13668:
13658:
13648:
13620:
13547:
13537:
13527:
13426:
13416:
13406:
13378:
13360:
13350:
13340:
13131:
13121:
13111:
13023:
13004:
12994:
12984:
12451:
12441:
12431:
12403:
12385:
12375:
12365:
12289:
12279:
12269:
12114:
12095:
12085:
12075:
11586:
11576:
11566:
11538:
11520:
11510:
11500:
11353:
11334:
11324:
11314:
11140:
11122:
11112:
11102:
10946:
10936:
10926:
10880:
10870:
10860:
10842:
10814:
10804:
10794:
10766:
10748:
10738:
10728:
10341:
10312:
10302:
10292:
10091:
10005:
9995:
9985:
9909:
9899:
9889:
9290:
9280:
9270:
9129:
9119:
9109:
9090:
9080:
9070:
9042:
8564:
8554:
8544:
8516:
8498:
8488:
8478:
8364:
8354:
8188:
8149:
8128:
8118:
8108:
8089:
8079:
8069:
8050:
8040:
8030:
8011:
8001:
7991:
7398:
7388:
7378:
7350:
7322:
7276:
7266:
7256:
7228:
7210:
7200:
7190:
7162:
7144:
7134:
7124:
6654:
6644:
6634:
6493:
6483:
6473:
6251:
5967:
5934:
5901:
5868:
5835:
5802:
5769:
5736:
5685:
5652:
5591:
5538:
5505:
5472:
5439:
5417:
5407:
5397:
5368:
5278:
4990:
4980:
4970:
4947:
4937:
4927:
4904:
4894:
4884:
4861:
4851:
4841:
4819:
4790:
4780:
4770:
4728:
4718:
4708:
4685:
4675:
4665:
4641:
4631:
4621:
4598:
4588:
4578:
4555:
4545:
4535:
4512:
4502:
4492:
4470:
4460:
4450:
4368:
4358:
4348:
3931:
3879:
3869:
3840:
3830:
3783:
3773:
3744:
3734:
3687:
3677:
3648:
3638:
3609:
3599:
3503:
3475:
3465:
3426:
3408:
3398:
3388:
3365:
3355:
3345:
3274:
3256:
3246:
3236:
3213:
3203:
3193:
3165:
3150:
3117:
3099:
3089:
3079:
3056:
3046:
3036:
3013:
3003:
2993:
2907:
2868:
2858:
2829:
2819:
2790:
2780:
2751:
2741:
2712:
2702:
2673:
2663:
2461:
2451:
2321:
2303:
2293:
2283:
2250:
2232:
2222:
2212:
2103:
2085:
2075:
2065:
2032:
2014:
2004:
1994:
1966:
1951:
1923:
1908:
1875:
1857:
1847:
1837:
1804:
1786:
1776:
1766:
1522:
1499:
1484:
1437:
1422:
1367:
1357:
1347:
1306:
1291:
1257:
1247:
1237:
1155:
1145:
1135:
1093:
1083:
1073:
1045:
1002:
982:
959:
944:
921:
911:
901:
827:
817:
807:
775:
765:
755:
726:
706:
139:
129:
119:
17596:(Chapter 21, Naming the Archimedean and Catalan polyhedra and tilings, Architectonic and Catoptric tessellations, p 292-298, includes all the nonprismatic forms)
9582:
can be orthogonally projected into the euclidean plane with various symmetry arrangements. The highest (hexagonal) symmetry form projects into a nonuniform
17669:(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.
13235:
A double symmetry construction can be made by placing truncated octahedra on the truncated cuboctahedra, resulting in a nonuniform honeycomb with
1578:
can be orthogonally projected into the euclidean plane with various symmetry arrangements. The highest (hexagonal) symmetry form projects into a
9169:
A double symmetry construction can be made by placing octahedra on the truncated cubes, resulting in a nonuniform honeycomb with two kinds of
14726:
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.
8399:
A double symmetry construction can be made by placing octahedra on the cuboctahedra, resulting in a nonuniform honeycomb with two kinds of
4295:. A double symmetry construction can be constructed by placing a small cube into each large cube, resulting in a nonuniform honeycomb with
14743:
A double symmetry construction can be made by placing rhombicuboctahedra on the truncated cubes, resulting in a nonuniform honeycomb with
12301:
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.
4058:
14464:
55:
16559:
is constructed by removing alternating long rectangles from the octagons orthogonally and is not uniform, but it can be represented as
14063:
A double symmetry construction can be made by placing icosahedra on the rhombicuboctahedra, resulting in a nonuniform honeycomb with
17:
17489:
9547:
14616:, seen as boundary cells from a subset of cells. One has triangles and squares, and the other triangles, squares, and octagons.
388:
17646:
17593:
17707:
4381:
generates 15 permutations of uniform tessellations, 9 with distinct geometry including the alternated cubic honeycomb. The
16287:
is constructed by removing alternating long rectangles from the octagons and is not uniform, but it can be represented as
12812:
form can be drawn with one color for each cell type. The bifurcating diagram form can be drawn with two types (colors) of
17641:, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
6938:
4047:
4052:
4042:
5998:
5301:
generates 9 permutations of uniform tessellations, 4 with distinct geometry including the alternated cubic honeycomb.
17612:
18104:
18087:
12200:
A double symmetry construction can be made by placing cuboctahedra on the rhombicuboctahedra, which results in the
11191:
9555:
9443:
4278:
3919:
16015:
Individual cells have 2-fold rotational symmetry. In 2D orthogonal projection, this looks like a mirror symmetry.
4385:
cubic honeycomb (also known as the runcinated cubic honeycomb) is geometrically identical to the cubic honeycomb.
18525:
18163:
2429:
18598:
13867:
5986:
4737:
4694:
4037:
3453:
2200:
1982:
1754:
18583:
17624:(Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
5258:
2271:
2053:
18588:
18537:
13494:
15942:
15577:
11787:
11716:
9482:
7058:
6067:
5953:
5920:
5557:
5235:
4999:
4650:
468:
458:
17984:
17869:
17826:
17783:
17740:
18593:
17494:
14771:
14478:
14347:
11054:
9762:. These uniform symmetries can be represented by coloring differently the cells in each construction.
8408:
6379:
6041:
5671:
5458:
5062:
4194:
2885:
1825:
17948:
17912:
17405:
of the truncated square prismatic honeycomb, although it can not be made uniform, but it can be given
15266:
15228:
14982:
14690:
14287:
13559:
13143:
12881:
12841:
12549:
12004:
11964:
11676:
11014:
10200:
10132:
10036:
9940:
9842:
9754:. This honeycomb has four uniform constructions, with the truncated octahedral cells having different
9718:
9400:
8950:
8912:
8663:
7863:
7824:
7785:
7746:
7496:
7003:
6965:
6883:
6845:
6708:
6667:
6506:
6315:
6274:
6149:
6004:
223:
18319:
18264:
18215:
17649:
17499:
9583:
6772:
5887:
5854:
5821:
5324:
4607:
4564:
4408:
4306:
symmetry). Its vertex figure is a triangular pyramid with its lateral faces augmented by tetrahedra.
4267:
4256:
3857:
3818:
463:
449:
17368:
438:
Simple cubic lattices can be distorted into lower symmetries, represented by lower crystal systems:
18082:
17733:
17700:
17603:
17193:
17170:
16923:
16900:
16646:
16389:
16104:
15946:
15604:
14816:
14128:
13797:
13308:
13214:
12329:
11464:
11187:. These have symmetry , and respectively. The first and last symmetry can be doubled as ] and ].
11060:
10694:
9533:
9234:
8442:
7084:
453:
423:
380:
15484:
13221:
12711:
12169:
11832:, shown here with cubic symmetry, with atoms placed at the center of the cells of this honeycomb.
18114:
17504:
16893:
15828:
15506:
15205:
15064:
14886:
13499:
12813:
12651:
12467:
9591:
9587:
9502:
9177:(tetragonal disphenoids and digonal disphenoids). The vertex figure is an octakis square cupola.
6564:
5147:
4324:, two kinds of tetragonal disphenoids, triangular pyramids, and sphenoids. Its vertex figure has
3376:
3333:
3224:
3181:
1683:
16237:
14954:
14509:
13059:
12529:
10516:
9373:
17402:
17220:
16942:
16673:
15781:
of the omnitruncated cubic honeycomb, although it can not be made uniform, but it can be given
15778:
14778:
13270:
12680:
12609:
12254:
11829:
9704:
9563:
9257:
9148:
6413:
5704:
5524:
5491:
4956:
4913:
4320:
The resulting honeycomb can be alternated to produce another nonuniform honeycomb with regular
384:
328:
15536:
14090:
10998:
18563:
18556:
18549:
18371:
18309:
18254:
18205:
18143:
17581:
14381:
9510:
9358:
8250:
17105:
16506:
16259:
13688:
4291:
The cubic honeycomb has a lower symmetry as a runcinated cubic honeycomb, with two sizes of
18513:
18506:
18501:
17474:
17137:
16867:
15529:
15475:
15466:
15119:
can be orthogonally projected into the euclidean plane with various symmetry arrangements.
15060:
14959:
14789:
14527:
can be orthogonally projected into the euclidean plane with various symmetry arrangements.
14460:
14385:
13970:
13281:
13236:
13201:
12727:
can be orthogonally projected into the euclidean plane with various symmetry arrangements.
12655:
12647:
12476:
11847:
can be orthogonally projected into the euclidean plane with various symmetry arrangements.
11754:
10633:
10618:
10402:
9759:
9517:
9506:
9498:
9490:
9378:
9306:
8798:
can be orthogonally projected into the euclidean plane with various symmetry arrangements.
8742:
8243:
7725:
7635:
can be orthogonally projected into the euclidean plane with various symmetry arrangements.
7579:
4870:
4382:
473:
347:
308:
15547:
14101:
13923:
10530:
9689:
9682:
9675:
9668:
9661:
9181:
8:
18416:
18354:
18349:
18292:
18287:
18237:
18232:
18188:
18183:
18131:
17693:
17681:
16601:
16459:
16329:
16174:
16000:
15724:
14744:
14405:
14389:
14269:
14198:
14023:
11758:
11602:
10523:
9708:
8332:
8320:
7608:
7537:
408:
65:
16535:
17577:
17163:
16886:
15454:
15089:
15081:
15072:
15022:
14950:
14939:
14613:
14470:
14408:
14328:
14272:
12672:
12590:
11779:
11652:
10667:
9712:
9567:
9539:
9369:
9339:
8763:
8640:
7600:
7473:
4310:
427:
376:
336:
266:
200:
17667:
Sulle reti di poliedri regolari e semiregolari e sulle corrispondenti reti correlative
17628:
17200:
16930:
16653:
16396:
16111:
15867:
15611:
15435:
14823:
14264:
14135:
13945:
13804:
13315:
13052:
12524:
12336:
11471:
10701:
9241:
9192:
8449:
7091:
4229:
4111:
4104:
4097:
3577:
3570:
3563:
2634:
2627:
2620:
1675:
870:
412:
332:
96:
18361:
18299:
18244:
18195:
18173:
18153:
18035:
17721:
17717:
17642:
17608:
17589:
17388:
17141:
17116:
16871:
16846:
16546:
16270:
15931:
15760:
15450:
15428:
15039:
14934:
14609:
14364:
13956:
13570:
13197:
12663:
12626:
12534:
12208:, square antiprism pairs and zero-height tetragonal disphenoids as components of the
11733:
11071:
9649:
9642:
9635:
9628:
9621:
9529:
9494:
9460:
9321:
8721:
8328:
7554:
4245:
4172:
3761:
2922:
2807:
1579:
1457:
1396:
312:
287:
283:
17674:
17567:
14594:
14587:
14580:
12794:
12787:
12780:
10502:
9353:
18136:
18072:
17662:
17458:
17376:
17327:
17149:
17058:
16359:
16205:
15957:
15832:
15737:
15683:
15562:
15557:
This honeycomb can then be alternated to produce another nonuniform honeycomb with
15221:
15186:
15179:
15172:
14756:
14568:
14561:
14554:
14072:
14045:
13889:
13248:
12768:
12761:
12754:
12306:
12233:
12217:
12162:
11929:
11770:
11722:
11641:
11636:
10639:
This honeycomb can then be alternated to produce another nonuniform honeycomb with
10509:
8880:
8404:
8378:
8257:
7738:
7717:
6074:
4183:
4161:
3997:
2956:
2846:
2768:
1724:
1687:
856:
847:
640:
392:
17156:
15160:
15153:
15146:
14731:
14353:
13733:
13262:(as tetragonal disphenoids). Its vertex figure is topologically equivalent to the
12963:
12298:, containing faces from two of four hyperplanes of the cubic fundamental domain.
8415:
17510:
17462:
17406:
16875:
16780:
16560:
16410:
16288:
16125:
15980:
15881:
15836:
15782:
15625:
15552:
15514:
15510:
15357:
15349:
15342:
15209:
15201:
15068:
14895:
14837:
14794:
14647:
14502:
14418:
14397:
14216:
14149:
14106:
13982:
13818:
13609:
13327:
13286:
13240:
13099:
12971:
12956:
12809:
12352:
12258:
12062:
11914:
11907:
11900:
11487:
11282:
11194:. The centers of the icosahedra are located at the fcc positions of the lattice.
11090:
10715:
10622:
10260:
9525:
9521:
9464:
9197:
9155:
9029:
8623:
8465:
8420:
8236:
7976:
7729:
7558:
7457:
7111:
4315:
2951:
2929:
1719:
865:
680:
106:
12228:(as tetragonal disphenoids), with a vertex figure topologically equivalent to a
11888:
11881:
11874:
6435:
2592:
18403:
18396:
18389:
18336:
18329:
18274:
18030:
17632:
14770:(as digonal disphenoids). Its vertex figure is topologically equivalent to the
14393:
14207:
14083:
13184:
12615:
12148:
10603:
10596:
10589:
10575:
8865:
8858:
8851:
8754:
8746:
8629:
8580:
7702:
7695:
7688:
4069:
3717:
3535:
485:
444:
362:, so that there are no gaps. It is an example of the more general mathematical
14488:
12688:
12141:
11816:
10582:
8839:
8832:
8825:
7676:
7669:
7662:
6793:
6110:
18577:
18062:
18052:
18042:
17543:
17086:
16817:
16615:: square prisms and rectangular trapezoprisms (topologically equivalent to a
16520:
16500:
16347:: square prisms and rectangular trapezoprisms (topologically equivalent to a
16245:
16191:
15678:
15582:
15541:
15422:
15097:
15075:
14974:
14928:
14890:
14783:
14411:
14279:
14258:
14095:
13931:
13917:
13884:
13507:
13488:
13455:
13446:
13275:
13046:
12833:
12666:
12541:
12518:
12471:
12213:
12209:
12156:
11956:
11933:
11773:
11762:
11668:
11611:
11263:
11006:
10975:
10496:
10488:
10482:
10473:
10467:
10461:
10455:
10446:
9835:
9755:
9751:
9513:
9393:
9347:
9186:
9142:
9014:
8904:
8884:
8757:
8656:
8617:
8230:
7968:
7961:
7954:
7721:
7594:
7587:
7489:
7451:
7414:
6586:
6037:
5298:
4378:
3585:
1697:
1583:
1326:
1174:
504:
416:
320:
319:
cells. It has 4 cubes around every edge, and 8 cubes around each vertex. Its
261:
216:
178:
16467:
16182:
15729:
15573:(as tetragonal disphenoids, phyllic disphenoids, and irregular tetrahedra).
14211:
14202:
13875:
12480:
11606:
10440:
10434:
10425:
10419:
10410:
9449:
9310:
9021:
8584:
8386:
7947:
4251:
3813:
17340:
17133:
16863:
15696:
15056:
15028:
13606:(as tetragonal disphenoids), and new tetrahedral cells created at the gaps.
13464:
12643:
11795:
11750:
11615:
10966:
9486:
9477:
The bitruncated cubic honeycomb shown here in relation to a cubic honeycomb
9217:
8738:
8593:
7591:
7575:
7462:
7427:
7418:
4150:
2729:
396:
368:
304:
159:
7720:
for the cells of this honeycomb with reflective symmetry, listed by their
1557:
1108:
1017:
44:
17466:
17336:
15950:
15840:
15692:
15570:
15304:
14946:
14767:
14324:
14064:
14034:
13880:
13603:
13592:
13460:
13451:
13259:
12918:
12586:
12225:
12041:
11648:
11203:
10971:
10962:
10648:
10640:
9771:
9559:
9365:
9334:
9174:
8989:
8778:
8771:
8704:
8636:
7900:
7615:
7543:
7469:
6055:
5312:
4396:
4321:
4234:
4212:
4128:
3722:
3626:
2651:
860:
602:
516:
196:
16008:
14621:
16512:
15566:
15491:
14748:
14626:
14068:
13263:
12221:
12205:
10644:
9170:
8750:
8710:
8589:
8400:
7583:
7423:
4240:
4223:
4218:
4156:
3756:
3665:
3660:
2763:
1694:
1668:
355:
324:
189:
184:
11936:, the second seen with alternately colored rhombicuboctahedral cells.
8403:(regular octahedra and triangular antiprisms). The vertex figure is a
16340:
16187:
15824:
15674:
15558:
15325:
13974:
13588:
13442:
12939:
11241:
10663:
9813:
6062:
5319:
4403:
4090:
3024:
2613:
1671:
1653:
1646:
1639:
480:
16835:
16078:
16071:
16064:
16057:
16048:
16041:
4167:
2802:
1627:
1620:
1613:
272:
17351:
17331:
17073:
17062:
17053:
16793:
16487:
16476:
16220:
16209:
16200:
15707:
15687:
14240:
14229:
13904:
13893:
13475:
12489:
11624:
10986:
10671:
10659:
8604:
7438:
6203:
4083:
3989:
3556:
3549:
2946:
2606:
1714:
16784:
15750:
14899:
14495:
14220:
8887:, the second seen with alternately colored truncated cubic cells.
4273:
4076:
3914:
3542:
2599:
39:
17599:
16809:
16025:
14920:
14915:
14250:
12510:
12505:
9326:
8609:
8324:
6040:. The symmetry can be multiplied by the symmetry of rings in the
4331:
symmetry and has 26 triangular faces, 39 edges, and 15 vertices.
15846:
13981:(square prisms). It is not uniform but it can be represented as
13608:
Although it is not uniform, constructionally it can be given as
4262:
3852:
17356:
17078:
16804:
16492:
16225:
15712:
14910:
14245:
13909:
13480:
12500:
9473:
9173:(regular octahedra and triangular antiprisms) and two kinds of
7443:
4145:
4027:
2724:
587:
573:
497:
491:
170:
13140:. This honeycomb cells represents the fundamental domains of
12694:
11800:
4207:
4189:
4178:
4123:
3621:
2880:
2841:
2646:
17515:
16034:
15993:
15970:
14459:
with three ringed nodes representing 3 active mirrors in the
11823:
4134:
2685:
580:
566:
15992:
is a space-filling honeycomb constructed as the dual of the
15103:
13292:
4299:, square prisms, and rectangular trapezoprisms (a cube with
17470:
17145:
17049:
16879:
16789:
16616:
16612:
16472:
16348:
16344:
16196:
15588:
15518:
14752:
14401:
14225:
13978:
13244:
12808:
Cells can be shown in two different symmetries. The linear
12659:
12485:
12229:
11766:
11620:
8783:
7620:
4296:
4292:
4139:
2926:
2690:
509:
316:
155:
17546:
9215:
37:
10678:
16088:
15528:-symmetric variants). Its vertex figure is an irregular
11190:
This honeycomb is represented in the boron atoms of the
9562:
can not tessellate space alone, this dual has identical
9223:
594:
16630:
17177:
10625:(as ditrigonal trapezoprisms). Its vertex figure is a
433:
17987:
17951:
17915:
17872:
17829:
17786:
17743:
15269:
15231:
14985:
14693:
14290:
13146:
12884:
12844:
12552:
12204:, by taking the triangular antiprism gaps as regular
12007:
11967:
11679:
11017:
10203:
10135:
10039:
9943:
9845:
9721:
9586:. A square symmetry projection forms two overlapping
9403:
8953:
8915:
8666:
7866:
7827:
7788:
7749:
7499:
7006:
6968:
6886:
6848:
6711:
6670:
6509:
6318:
6277:
6152:
6007:
1693:
It is in a sequence of polychora and honeycombs with
226:
15200:
Cells can be shown in two different symmetries. The
850:, derived from different symmetries. These include:
13191:
9528:, with 2 hexagons and one square on each edge, and
1662:
27:
Only regular space-filling tessellation of the cube
18015:
17973:
17937:
17900:
17857:
17814:
17771:
17639:Kaleidoscopes: Selected Writings of H.S.M. Coxeter
17507:A hyperbolic cubic honeycomb with 5 cubes per edge
16907:
15291:
15253:
15007:
14715:
14312:
13168:
12906:
12866:
12574:
12029:
11989:
11701:
11039:
10225:
10157:
10061:
9965:
9867:
9743:
9425:
8975:
8937:
8688:
7888:
7849:
7810:
7771:
7521:
7028:
6990:
6908:
6870:
6733:
6692:
6531:
6340:
6299:
6174:
6029:
4334:
248:
14112:
12313:
1682:cubes around each edge. It's also related to the
18575:
15517:(as ditrigonal trapezoprisms), and two kinds of
14800:
399:to form a uniform honeycomb in spherical space.
15569:(as triangular antiprisms), and three kinds of
1678:{4,3,3}, which exists in 4-space, and only has
375:Honeycombs are usually constructed in ordinary
16373:
15999:24 cells fit around a vertex, making a chiral
15854:Dual alternated omnitruncated cubic honeycomb
13781:
12240:
12201:
11448:
9203:
17701:
17675:"3D Euclidean Honeycombs x4o3o4o - chon - O1"
15990:dual alternated omnitruncated cubic honeycomb
15847:Dual alternated omnitruncated cubic honeycomb
15751:Dual alternated omnitruncated cubic honeycomb
14687:. Faces exist in 3 of 4 hyperplanes of the ,
14633:
415:of the form {4,3,...,3,4}, starting with the
14603:
8426:
7068:
17184:
16914:
16637:
16380:
16095:
15853:
15595:
15063:) in Euclidean 3-space. It is composed of
14807:
14388:) in Euclidean 3-space. It is composed of
14119:
13788:
13299:
12320:
11757:) in Euclidean 3-space. It is composed of
11455:
10685:
9210:
8745:) in Euclidean 3-space. It is composed of
8433:
7582:) in Euclidean 3-space. It is composed of
7075:
407:It is part of a multidimensional family of
32:
17708:
17694:
17181:
16911:
16634:
16377:
16092:
15850:
15592:
14804:
14116:
13785:
13300:Alternated cantitruncated cubic honeycomb
13296:
12317:
11452:
10682:
9703:The vertex figure for this honeycomb is a
9207:
8430:
8327:centers of the cuboctahedra, creating two
7072:
29:
17615:p. 296, Table II: Regular honeycombs
16003:that can be stacked in all 3-dimensions:
15596:Alternated omnitruncated cubic honeycomb
13581:alternated cantitruncated cubic honeycomb
13293:Alternated cantitruncated cubic honeycomb
13085:
514:
303:is the only proper regular space-filling
17490:Architectonic and catoptric tessellation
15994:alternated omnitruncated cubic honeycomb
15971:Alternated omnitruncated cubic honeycomb
15771:alternated omnitruncated cubic honeycomb
15589:Alternated omnitruncated cubic honeycomb
15521:(as rectangular trapezoprisms and their
9548:Architectonic and catoptric tessellation
9472:
17549:6-1 cases, skipping one with zero marks
16285:runcic cantitruncated cubic cellulation
10686:Alternated bitruncated cubic honeycomb
1582:. A square symmetry projection forms a
14:
18576:
17682:Uniform Honeycombs in 3-Space: 01-Chon
17607:, (3rd edition, 1973), Dover edition,
16096:Runcic cantitruncated cubic honeycomb
15500:
14738:
14058:
13230:
12195:
11082:alternated bitruncated cubic honeycomb
10679:Alternated bitruncated cubic honeycomb
10651:(as sphenoids). Its vertex figure has
10612:
9164:
8394:
17469:(as tetragonal disphenoids) from the
16638:Truncated square prismatic honeycomb
16281:runcic cantitruncated cubic honeycomb
16089:Runcic cantitruncated cubic honeycomb
12706:Four cells exist around each vertex:
12236:attached to one of its square faces.
8753:in a ratio of 1:1, with an isosceles
402:
17672:
17655:Regular and Semi Regular Polytopes I
17185:Snub square antiprismatic honeycomb
17100:Cairo pentagonal prismatic honeycomb
16856:truncated square prismatic honeycomb
16631:Truncated square prismatic honeycomb
16369:-symmetry wedges) filling the gaps.
15444:
14055:-symmetry wedges) filling the gaps.
10670:(divided into two sets of 2), and 4
4286:
841:
17558:Williams, 1979, p 199, Figure 5-38.
17399:snub square antiprismatic honeycomb
17178:Snub square antiprismatic honeycomb
12650:) in Euclidean 3-space, made up of
434:Isometries of simple cubic lattices
24:
18016:{\displaystyle {\tilde {E}}_{n-1}}
17901:{\displaystyle {\tilde {D}}_{n-1}}
17858:{\displaystyle {\tilde {B}}_{n-1}}
17815:{\displaystyle {\tilde {C}}_{n-1}}
17772:{\displaystyle {\tilde {A}}_{n-1}}
15862:Dual alternated uniform honeycomb
8335:is represented by Coxeter diagram
383:. They may also be constructed in
25:
18610:
17130:simo-square prismatic cellulation
16860:tomo-square prismatic cellulation
14755:(as square prisms), two kinds of
12224:(as triangular antipodiums), and
11940:Vertex uniform colorings by cell
11089:constructions from three related
8319:This honeycomb can be divided on
1553:t{∞}×t{∞}×t{∞}
17974:{\displaystyle {\tilde {F}}_{4}}
17938:{\displaystyle {\tilde {G}}_{2}}
17451:
17446:
17441:
17436:
17431:
17426:
17421:
17416:
17411:
17367:
17339:
17330:
17314:
17309:
17304:
17299:
17294:
17289:
17284:
17279:
17274:
17266:
17261:
17256:
17251:
17246:
17241:
17236:
17231:
17226:
17155:
17104:
17061:
17052:
17036:
17031:
17026:
17021:
17016:
17011:
17006:
17001:
16996:
16988:
16983:
16978:
16973:
16968:
16963:
16958:
16953:
16948:
16915:Snub square prismatic honeycomb
16885:
16834:
16830:Tetrakis square prismatic tiling
16792:
16783:
16767:
16762:
16757:
16752:
16747:
16742:
16737:
16732:
16727:
16719:
16714:
16709:
16704:
16699:
16694:
16689:
16684:
16679:
16594:
16589:
16584:
16579:
16574:
16569:
16564:
16534:
16505:
16475:
16466:
16446:
16441:
16436:
16431:
16426:
16421:
16416:
16322:
16317:
16312:
16307:
16302:
16297:
16292:
16258:
16236:
16208:
16199:
16190:
16181:
16161:
16156:
16151:
16146:
16141:
16136:
16131:
16077:
16070:
16063:
16056:
16047:
16040:
16033:
16024:
16007:
15930:
15917:
15912:
15907:
15902:
15897:
15892:
15887:
15817:
15812:
15807:
15802:
15797:
15792:
15787:
15728:
15723:
15695:
15686:
15677:
15661:
15656:
15651:
15646:
15641:
15636:
15631:
15576:
15546:
15535:
15490:
15483:
15474:
15465:
15434:
15427:
15412:
15407:
15402:
15393:
15388:
15383:
15378:
15373:
15368:
15363:
15348:
15341:
15292:{\displaystyle {\tilde {C}}_{3}}
15254:{\displaystyle {\tilde {C}}_{3}}
15185:
15178:
15171:
15159:
15152:
15145:
15110:
15102:
15096:
15027:
15008:{\displaystyle {\tilde {C}}_{3}}
14933:
14898:
14889:
14873:
14868:
14863:
14858:
14853:
14848:
14843:
14788:
14777:
14730:
14716:{\displaystyle {\tilde {C}}_{3}}
14681:
14676:
14671:
14666:
14661:
14656:
14651:
14625:
14620:
14593:
14586:
14579:
14567:
14560:
14553:
14518:
14508:
14501:
14494:
14487:
14453:
14448:
14443:
14438:
14433:
14428:
14423:
14378:runcitruncated cubic cellulation
14352:
14313:{\displaystyle {\tilde {C}}_{3}}
14263:
14228:
14219:
14210:
14201:
14185:
14180:
14175:
14170:
14165:
14160:
14155:
14100:
14089:
14016:
14011:
14006:
14001:
13996:
13991:
13986:
13944:
13922:
13892:
13883:
13874:
13854:
13849:
13844:
13839:
13834:
13829:
13824:
13769:
13764:
13759:
13754:
13749:
13744:
13739:
13732:
13724:
13719:
13714:
13709:
13704:
13699:
13694:
13687:
13671:
13666:
13661:
13656:
13651:
13646:
13641:
13633:
13628:
13623:
13618:
13613:
13558:
13550:
13545:
13540:
13535:
13530:
13525:
13520:
13498:
13493:
13463:
13454:
13445:
13429:
13424:
13419:
13414:
13409:
13404:
13399:
13391:
13386:
13381:
13376:
13371:
13363:
13358:
13353:
13348:
13343:
13338:
13333:
13280:
13269:
13220:
13213:
13192:Related polyhedra and honeycombs
13183:
13169:{\displaystyle {\tilde {B}}_{3}}
13134:
13129:
13124:
13119:
13114:
13109:
13104:
13058:
13051:
13036:
13031:
13026:
13021:
13016:
13007:
13002:
12997:
12992:
12987:
12982:
12977:
12962:
12955:
12907:{\displaystyle {\tilde {B}}_{3}}
12867:{\displaystyle {\tilde {C}}_{3}}
12793:
12786:
12779:
12767:
12760:
12753:
12718:
12710:
12693:
12687:
12640:cantitruncated cubic cellulation
12614:
12575:{\displaystyle {\tilde {C}}_{3}}
12528:
12523:
12488:
12479:
12470:
12454:
12449:
12444:
12439:
12434:
12429:
12424:
12416:
12411:
12406:
12401:
12396:
12388:
12383:
12378:
12373:
12368:
12363:
12358:
12305:
12292:
12287:
12282:
12277:
12272:
12267:
12262:
12168:
12161:
12147:
12140:
12127:
12122:
12117:
12112:
12107:
12098:
12093:
12088:
12083:
12078:
12073:
12068:
12030:{\displaystyle {\tilde {B}}_{3}}
11990:{\displaystyle {\tilde {C}}_{3}}
11932:by reflectional symmetry of the
11913:
11906:
11899:
11887:
11880:
11873:
11838:
11822:
11815:
11799:
11794:
11721:
11702:{\displaystyle {\tilde {C}}_{3}}
11635:
11623:
11614:
11605:
11589:
11584:
11579:
11574:
11569:
11564:
11559:
11551:
11546:
11541:
11536:
11531:
11523:
11518:
11513:
11508:
11503:
11498:
11493:
11414:
11409:
11404:
11399:
11394:
11385:
11380:
11375:
11366:
11361:
11356:
11351:
11346:
11337:
11332:
11327:
11322:
11317:
11312:
11307:
11298:
11293:
11288:
11181:
11176:
11171:
11166:
11161:
11153:
11148:
11143:
11138:
11133:
11125:
11120:
11115:
11110:
11105:
11100:
11095:
11059:
11040:{\displaystyle {\tilde {C}}_{3}}
10997:
10974:
10965:
10949:
10944:
10939:
10934:
10929:
10924:
10919:
10911:
10906:
10901:
10896:
10891:
10883:
10878:
10873:
10868:
10863:
10858:
10853:
10845:
10840:
10835:
10830:
10825:
10817:
10812:
10807:
10802:
10797:
10792:
10787:
10779:
10774:
10769:
10764:
10759:
10751:
10746:
10741:
10736:
10731:
10726:
10721:
10647:(as triangular antiprisms), and
10602:
10595:
10588:
10581:
10574:
10529:
10522:
10515:
10508:
10501:
10487:
10481:
10472:
10466:
10460:
10454:
10445:
10439:
10433:
10424:
10418:
10409:
10392:
10387:
10382:
10373:
10368:
10363:
10358:
10353:
10344:
10339:
10334:
10329:
10324:
10315:
10310:
10305:
10300:
10295:
10290:
10285:
10276:
10271:
10266:
10250:
10245:
10240:
10226:{\displaystyle {\tilde {A}}_{3}}
10190:
10185:
10180:
10175:
10170:
10158:{\displaystyle {\tilde {A}}_{3}}
10122:
10117:
10112:
10107:
10102:
10094:
10089:
10084:
10079:
10074:
10062:{\displaystyle {\tilde {B}}_{3}}
10026:
10021:
10016:
10008:
10003:
9998:
9993:
9988:
9983:
9978:
9966:{\displaystyle {\tilde {C}}_{3}}
9930:
9925:
9920:
9912:
9907:
9902:
9897:
9892:
9887:
9882:
9868:{\displaystyle {\tilde {C}}_{3}}
9744:{\displaystyle {\tilde {A}}_{3}}
9688:
9681:
9674:
9667:
9660:
9648:
9641:
9634:
9627:
9620:
9573:
9556:disphenoid tetrahedral honeycomb
9448:
9444:Disphenoid tetrahedral honeycomb
9426:{\displaystyle {\tilde {C}}_{3}}
9352:
9309:
9293:
9288:
9283:
9278:
9273:
9268:
9263:
9222:
9216:
9191:
9180:
9154:
9147:
9132:
9127:
9122:
9117:
9112:
9107:
9102:
9093:
9088:
9083:
9078:
9073:
9068:
9063:
9055:
9050:
9045:
9040:
9035:
9020:
9013:
8976:{\displaystyle {\tilde {C}}_{3}}
8938:{\displaystyle {\tilde {B}}_{3}}
8883:by reflectional symmetry of the
8864:
8857:
8850:
8838:
8831:
8824:
8789:
8782:
8777:
8709:
8689:{\displaystyle {\tilde {C}}_{3}}
8622:
8592:
8583:
8567:
8562:
8557:
8552:
8547:
8542:
8537:
8529:
8524:
8519:
8514:
8509:
8501:
8496:
8491:
8486:
8481:
8476:
8471:
8414:
8385:
8367:
8362:
8357:
8352:
8347:
8342:
8337:
8256:
8249:
8242:
8235:
8220:
8215:
8210:
8205:
8200:
8191:
8186:
8181:
8176:
8171:
8162:
8157:
8152:
8147:
8142:
8131:
8126:
8121:
8116:
8111:
8106:
8101:
8092:
8087:
8082:
8077:
8072:
8067:
8062:
8053:
8048:
8043:
8038:
8033:
8028:
8023:
8014:
8009:
8004:
7999:
7994:
7989:
7984:
7967:
7960:
7953:
7946:
7889:{\displaystyle {\tilde {A}}_{3}}
7850:{\displaystyle {\tilde {B}}_{3}}
7811:{\displaystyle {\tilde {B}}_{3}}
7772:{\displaystyle {\tilde {C}}_{3}}
7701:
7694:
7687:
7675:
7668:
7661:
7626:
7619:
7614:
7542:
7522:{\displaystyle {\tilde {C}}_{3}}
7456:
7426:
7417:
7401:
7396:
7391:
7386:
7381:
7376:
7371:
7363:
7358:
7353:
7348:
7343:
7335:
7330:
7325:
7320:
7315:
7307:
7302:
7297:
7292:
7287:
7279:
7274:
7269:
7264:
7259:
7254:
7249:
7241:
7236:
7231:
7226:
7221:
7213:
7208:
7203:
7198:
7193:
7188:
7183:
7175:
7170:
7165:
7160:
7155:
7147:
7142:
7137:
7132:
7127:
7122:
7117:
7050:
7045:
7040:
7029:{\displaystyle {\tilde {C}}_{3}}
6991:{\displaystyle {\tilde {A}}_{3}}
6930:
6925:
6920:
6909:{\displaystyle {\tilde {C}}_{3}}
6871:{\displaystyle {\tilde {A}}_{3}}
6834:
6829:
6824:
6815:
6810:
6805:
6792:
6764:
6759:
6754:
6749:
6744:
6734:{\displaystyle {\tilde {C}}_{3}}
6693:{\displaystyle {\tilde {A}}_{3}}
6657:
6652:
6647:
6642:
6637:
6632:
6627:
6618:
6613:
6608:
6603:
6598:
6585:
6556:
6551:
6546:
6532:{\displaystyle {\tilde {A}}_{3}}
6496:
6491:
6486:
6481:
6476:
6471:
6466:
6457:
6452:
6447:
6434:
6405:
6400:
6395:
6390:
6385:
6371:
6366:
6361:
6356:
6351:
6341:{\displaystyle {\tilde {B}}_{3}}
6300:{\displaystyle {\tilde {A}}_{3}}
6264:
6259:
6254:
6249:
6244:
6235:
6230:
6225:
6220:
6215:
6202:
6175:{\displaystyle {\tilde {A}}_{3}}
6139:
6134:
6129:
6124:
6119:
6109:
6030:{\displaystyle {\tilde {A}}_{3}}
5999:five distinct uniform honeycombs
5980:
5975:
5970:
5965:
5960:
5947:
5942:
5937:
5932:
5927:
5914:
5909:
5904:
5899:
5894:
5881:
5876:
5871:
5866:
5861:
5848:
5843:
5838:
5833:
5828:
5815:
5810:
5805:
5800:
5795:
5782:
5777:
5772:
5767:
5762:
5749:
5744:
5739:
5734:
5729:
5698:
5693:
5688:
5683:
5678:
5665:
5660:
5655:
5650:
5645:
5633:
5628:
5623:
5618:
5613:
5604:
5599:
5594:
5589:
5584:
5551:
5546:
5541:
5536:
5531:
5518:
5513:
5508:
5503:
5498:
5485:
5480:
5475:
5470:
5465:
5452:
5447:
5442:
5437:
5432:
5420:
5415:
5410:
5405:
5400:
5395:
5390:
5381:
5376:
5371:
5366:
5361:
5291:
5286:
5281:
5276:
5271:
5252:
5247:
5242:
5229:
5224:
5219:
5206:
5201:
5196:
5183:
5178:
5173:
5141:
5136:
5131:
5119:
5114:
5109:
5100:
5095:
5090:
5056:
5051:
5046:
5034:
5029:
5024:
4993:
4988:
4983:
4978:
4973:
4968:
4963:
4950:
4945:
4940:
4935:
4930:
4925:
4920:
4907:
4902:
4897:
4892:
4887:
4882:
4877:
4864:
4859:
4854:
4849:
4844:
4839:
4834:
4822:
4817:
4812:
4807:
4802:
4793:
4788:
4783:
4778:
4773:
4768:
4763:
4731:
4726:
4721:
4716:
4711:
4706:
4701:
4688:
4683:
4678:
4673:
4668:
4663:
4658:
4644:
4639:
4634:
4629:
4624:
4619:
4614:
4601:
4596:
4591:
4586:
4581:
4576:
4571:
4558:
4553:
4548:
4543:
4538:
4533:
4528:
4515:
4510:
4505:
4500:
4495:
4490:
4485:
4473:
4468:
4463:
4458:
4453:
4448:
4443:
4371:
4366:
4361:
4356:
4351:
4346:
4341:
4309:
4272:
4261:
4250:
4239:
4228:
4217:
4206:
4188:
4177:
4166:
4155:
4144:
4133:
4122:
4110:
4103:
4096:
4089:
4082:
4075:
4068:
3967:
3962:
3957:
3952:
3944:
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3659:
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3597:
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3496:
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3305:
3300:
3295:
3287:
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3267:
3259:
3254:
3249:
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3234:
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3216:
3211:
3206:
3201:
3196:
3191:
3186:
3173:
3168:
3163:
3158:
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3148:
3143:
3138:
3130:
3125:
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3115:
3110:
3102:
3097:
3092:
3087:
3082:
3077:
3072:
3059:
3054:
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3029:
3016:
3011:
3006:
3001:
2996:
2991:
2986:
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2900:
2895:
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2879:
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2866:
2861:
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2568:
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2500:
2492:
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2205:
2192:
2187:
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2177:
2172:
2167:
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2154:
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2139:
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2129:
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2116:
2111:
2106:
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2096:
2088:
2083:
2078:
2073:
2068:
2063:
2058:
2045:
2040:
2035:
2030:
2025:
2017:
2012:
2007:
2002:
1997:
1992:
1987:
1974:
1969:
1964:
1959:
1954:
1949:
1944:
1939:
1931:
1926:
1921:
1916:
1911:
1906:
1901:
1896:
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1883:
1878:
1873:
1868:
1860:
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1817:
1812:
1807:
1802:
1797:
1789:
1784:
1779:
1774:
1769:
1764:
1759:
1663:Related polytopes and honeycombs
1652:
1645:
1638:
1626:
1619:
1612:
1556:
1545:
1540:
1535:
1530:
1525:
1520:
1515:
1507:
1502:
1497:
1492:
1487:
1482:
1477:
1472:
1456:
1453:t{∞}×t{∞}×{∞}
1445:
1440:
1435:
1430:
1425:
1420:
1415:
1410:
1395:
1380:
1375:
1370:
1365:
1360:
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1314:
1309:
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1128:
1107:
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1066:
1058:
1053:
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1043:
1038:
1016:
1005:
1000:
995:
990:
985:
980:
975:
967:
962:
957:
952:
947:
942:
937:
932:
924:
919:
914:
909:
904:
899:
894:
830:
825:
820:
815:
810:
805:
800:
788:
783:
778:
773:
768:
763:
758:
753:
748:
739:
734:
729:
724:
719:
714:
709:
704:
699:
694:
689:
593:
586:
579:
572:
565:
271:
249:{\displaystyle {\tilde {C}}_{3}}
183:
158:
142:
137:
132:
127:
122:
117:
112:
43:
38:
17657:, (1.9 Uniform space-fillings)
17384:
17375:
17363:
17347:
17323:
17219:
17199:
17189:
17126:snub square prismatic honeycomb
17112:
17095:
17085:
17069:
17045:
16941:
16929:
16919:
16908:Snub square prismatic honeycomb
16842:
16825:
16816:
16800:
16776:
16672:
16652:
16642:
16542:
16529:
16519:
16499:
16483:
16455:
16409:
16395:
16385:
16266:
16253:
16244:
16232:
16216:
16170:
16124:
16110:
16100:
15976:
15966:
15956:
15938:
15926:
15880:
15866:
15858:
15756:
15746:
15736:
15719:
15703:
15670:
15624:
15610:
15600:
15053:omnitruncated cubic cellulation
15035:
15018:
14973:
14945:
14927:
14906:
14882:
14836:
14822:
14812:
14404:in a ratio of 1:1:3:3, with an
14360:
14343:
14323:
14278:
14257:
14236:
14194:
14148:
14134:
14124:
14120:Runcitruncated cubic honeycomb
13969:is constructed by snubbing the
13952:
13939:
13930:
13916:
13900:
13863:
13817:
13803:
13793:
13587:contains three types of cells:
13566:
13515:
13506:
13487:
13471:
13438:
13326:
13314:
13304:
13243:(as ditrigonal trapezoprisms),
12622:
12605:
12585:
12540:
12517:
12496:
12463:
12351:
12335:
12325:
12321:Cantitruncated cubic honeycomb
11729:
11712:
11667:
11647:
11631:
11598:
11486:
11470:
11460:
11067:
11050:
11005:
10993:
10982:
10958:
10714:
10700:
10690:
9766:Five uniform colorings by cell
9456:
9437:
9392:
9364:
9346:
9333:
9317:
9302:
9256:
9240:
9230:
8717:
8700:
8655:
8635:
8616:
8600:
8576:
8464:
8448:
8438:
7550:
7533:
7488:
7468:
7450:
7434:
7410:
7110:
7090:
7080:
4335:Related Euclidean tessellations
1690:with 5 cubes around each edge.
279:
260:
215:
195:
177:
166:
151:
105:
95:
71:
61:
51:
17995:
17959:
17923:
17880:
17837:
17794:
17751:
17631:, Uniform tilings of 3-space.
17561:
17552:
17537:
17528:
17473:, and two tetrahedra from the
15277:
15239:
14993:
14808:Omnitruncated cubic honeycomb
14701:
14640:runcitruncated cubic honeycomb
14525:runcitruncated cubic honeycomb
14374:runcitruncated cubic honeycomb
14298:
14113:Runcitruncated cubic honeycomb
13585:snub rectified cubic honeycomb
13154:
13092:cantitruncated cubic honeycomb
12892:
12852:
12828:Omnitruncated alternate cubic
12725:cantitruncated cubic honeycomb
12636:cantitruncated cubic honeycomb
12560:
12314:Cantitruncated cubic honeycomb
12015:
11975:
11951:Bicantellated alternate cubic
11687:
11025:
10211:
10143:
10047:
9951:
9853:
9729:
9590:, which combine together as a
9550:list, with its dual called an
9411:
8961:
8923:
8896:Bicantellated alternate cubic
8674:
7874:
7835:
7796:
7757:
7507:
7014:
6976:
6894:
6856:
6719:
6678:
6517:
6326:
6285:
6160:
6015:
1686:, Schläfli symbol {4,3,5}, of
1569:
234:
13:
1:
17521:
15823:and has symmetry ]. It makes
15195:
15117:omnitruncated cubic honeycomb
15049:omnitruncated cubic honeycomb
14801:Omnitruncated cubic honeycomb
14417:Its name is derived from its
12803:
11923:
11828:It is closely related to the
11747:cantellated cubic cellulation
9834:
9698:
9516:. Being composed entirely of
8874:
1667:It is related to the regular
389:hyperbolic uniform honeycombs
372:in any number of dimensions.
17620:Uniform Panoploid Tetracombs
17457:and has symmetry . It makes
16381:Biorthosnub cubic honeycomb
16022:
15420:
15336:
14751:(as triangular antiprisms),
14071:(as triangular antiprisms),
13685:
13065:
12950:
12818:
12662:in a ratio of 1:1:3, with a
12175:
12135:
11938:
11811:
11769:in a ratio of 1:1:3, with a
11456:Cantellated cubic honeycomb
11422:
11280:
10536:
10494:
10400:
9211:Bitruncated cubic honeycomb
9140:
9027:
9008:
8889:
8263:
8228:
8139:
7974:
7941:
7734:
1466:
1405:
1335:
1225:
1183:
1117:
1026:
883:
678:
638:
600:
560:
478:
7:
17653:(Paper 22) H.S.M. Coxeter,
17568:cantic snub cubic honeycomb
17483:
16611:symmetry) and two kinds of
16557:biorthosnub cubic honeycomb
16374:Biorthosnub cubic honeycomb
15943:pentagonal icositetrahedron
15055:is a uniform space-filling
13967:cantic snub cubic honeycomb
13782:Cantic snub cubic honeycomb
12701:
12642:is a uniform space-filling
12251:quarter oblate octahedrille
12247:cantellated cubic honeycomb
12241:Quarter oblate octahedrille
12212:. Other variants result in
11845:cantellated cubic honeycomb
11788:quarter oblate octahedrille
11749:is a uniform space-filling
11743:cantellated cubic honeycomb
11717:quarter oblate octahedrille
11449:Cantellated cubic honeycomb
11192:α-rhombohedral crystal
10658:symmetry and consists of 2
9580:bitruncated cubic honeycomb
9483:bitruncated cubic honeycomb
9204:Bitruncated cubic honeycomb
8737:is a uniform space-filling
8735:truncated cubic cellulation
8409:elongated square bipyramids
7711:
7574:is a uniform space-filling
7572:rectified cubic cellulation
3981:{p,3,p} regular honeycombs
2938:{4,3,p} regular honeycombs
1706:{p,3,4} regular honeycombs
846:There is a large number of
10:
18615:
17495:Alternated cubic honeycomb
15071:in a ratio of 1:3, with a
14772:augmented triangular prism
14644:square quarter pyramidille
14634:Square quarter pyramidille
14479:square quarter pyramidille
14382:space-filling tessellation
14348:square quarter pyramidille
13973:in a way that leaves only
13789:Orthosnub cubic honeycomb
12831:
11954:
11948:Truncated cubic honeycomb
11813:
9833:
8902:
8899:Truncated cubic honeycomb
8434:Truncated cubic honeycomb
8407:. The dual is composed of
7736:
7590:in a ratio of 1:1, with a
7076:Rectified cubic honeycomb
3980:
2937:
1705:
17689:
17500:List of regular polytopes
17171:convex uniform honeycombs
17162:It is constructed from a
16901:convex uniform honeycombs
16892:It is constructed from a
15136:
14604:Related skew apeirohedron
14544:
14463:from its relation to the
12744:
12202:rectified cubic honeycomb
11864:
11807:
11055:Ten-of-diamonds honeycomb
9611:
9584:rhombitrihexagonal tiling
9509:around each vertex, in a
8815:
8796:truncated cubic honeycomb
8731:truncated cubic honeycomb
8427:Truncated cubic honeycomb
7982:
7975:
7652:
7633:rectified cubic honeycomb
7568:rectified cubic honeycomb
7069:Rectified cubic honeycomb
6803:
6790:
6049:
5997:This honeycomb is one of
5306:
4390:
4018:
3996:
2977:
2955:
1745:
1723:
1603:
428:convex uniform polyhedral
381:convex uniform honeycombs
379:("flat") space, like the
18:Truncated cubic honeycomb
18083:Uniform convex honeycomb
17586:The Symmetries of Things
15947:tetragonal trapezohedron
15775:omnisnub cubic honeycomb
14766:-symmetric wedges), and
14082:-symmetric wedges), and
13258:-symmetric wedges), and
395:can be projected to its
339:called this honeycomb a
17505:Order-5 cubic honeycomb
16894:truncated square tiling
15204:form has two colors of
15123:Orthogonal projections
15084:calls this honeycomb a
14531:Orthogonal projections
14473:calls this honeycomb a
12814:truncated cuboctahedron
12731:Orthogonal projections
12675:calls this honeycomb a
11851:Orthogonal projections
11782:calls this honeycomb a
11198:Five uniform colorings
10641:pyritohedral icosahedra
9598:Orthogonal projections
9592:chamfered square tiling
9588:truncated square tiling
9542:calls this honeycomb a
8802:Orthogonal projections
8766:calls this honeycomb a
7639:Orthogonal projections
7603:calls this honeycomb a
6042:Coxeter–Dynkin diagrams
1684:order-5 cubic honeycomb
1590:Orthogonal projections
18017:
17975:
17939:
17902:
17859:
17816:
17773:
17401:can be constructed by
17221:Coxeter-Dynkin diagram
17166:extruded into prisms.
16943:Coxeter-Dynkin diagram
16896:extruded into prisms.
16674:Coxeter-Dynkin diagram
15829:truncated cuboctahedra
15777:can be constructed by
15507:truncated cuboctahedra
15293:
15255:
15216:Two uniform colorings
15206:truncated cuboctahedra
15065:truncated cuboctahedra
15009:
14717:
14314:
13170:
13096:triangular pyramidille
13086:Triangular pyramidille
12908:
12868:
12681:triangular pyramidille
12652:truncated cuboctahedra
12610:triangular pyramidille
12576:
12255:catoptric tessellation
12031:
11991:
11703:
11086:bisnub cubic honeycomb
11041:
10227:
10159:
10063:
9967:
9869:
9745:
9705:disphenoid tetrahedron
9564:disphenoid tetrahedron
9544:truncated octahedrille
9478:
9427:
9258:Coxeter-Dynkin diagram
8977:
8939:
8690:
7890:
7851:
7812:
7773:
7523:
7030:
6992:
6910:
6872:
6735:
6694:
6533:
6342:
6301:
6176:
6031:
419:, {4,4} in the plane.
358:or higher-dimensional
250:
18599:Regular tessellations
18457:Uniform 10-honeycomb
18018:
17976:
17940:
17903:
17860:
17817:
17774:
17582:Chaim Goodman-Strauss
17475:triangular bipyramids
17144:. It is composed of
16874:. It is composed of
15843:cells from the gaps.
15294:
15256:
15010:
14718:
14612:exists with the same
14406:isosceles-trapezoidal
14315:
14270:isosceles-trapezoidal
13171:
12909:
12869:
12825:Cantitruncated cubic
12577:
12032:
11992:
11704:
11042:
10228:
10160:
10064:
9968:
9870:
9760:Wythoff constructions
9746:
9707:, and it is also the
9558:. Although a regular
9511:tetragonal disphenoid
9476:
9428:
9359:tetragonal disphenoid
8978:
8940:
8691:
7891:
7852:
7813:
7774:
7524:
7031:
6993:
6911:
6873:
6736:
6695:
6534:
6343:
6302:
6177:
6032:
251:
18584:Regular 3-honeycombs
17985:
17949:
17913:
17870:
17827:
17784:
17741:
17622:, Manuscript (2006)
16513:Tetragonal antiwedge
15530:triangular bipyramid
15453:exist with the same
15449:Two related uniform
15267:
15229:
14983:
14691:
14608:Two related uniform
14461:Wythoff construction
14288:
13247:(as square prisms),
13202:vertex configuration
13144:
12882:
12842:
12550:
12005:
11965:
11830:perovskite structure
11677:
11015:
10634:triangular bipyramid
10201:
10133:
10037:
9941:
9843:
9719:
9552:oblate tetrahedrille
9505:cubes). It has four
9441:Oblate tetrahedrille
9401:
8951:
8913:
8664:
7864:
7825:
7786:
7747:
7726:Wythoff construction
7497:
7004:
6966:
6884:
6846:
6709:
6668:
6507:
6316:
6275:
6150:
6005:
2925:and honeycombs with
2921:It in a sequence of
409:hypercube honeycombs
385:non-Euclidean spaces
224:
18589:Regular 4-polytopes
18417:Uniform 9-honeycomb
18350:Uniform 8-honeycomb
18288:Uniform 7-honeycomb
18233:Uniform 6-honeycomb
18184:Uniform 5-honeycomb
18132:Uniform 4-honeycomb
17716:Fundamental convex
17673:Klitzing, Richard.
17152:in a ratio of 1:2.
17132:is a space-filling
16882:in a ratio of 1:1.
16862:is a space-filling
16020:
16001:octahedral symmetry
15217:
15124:
14532:
13971:truncated octahedra
13237:truncated octahedra
13209:
13196:It is related to a
12816:cells alternating.
12732:
12656:truncated octahedra
11941:
11852:
11199:
10668:isosceles triangles
10619:truncated octahedra
10403:truncated octahedra
9767:
9709:Goursat tetrahedron
9599:
9518:truncated octahedra
9507:truncated octahedra
9501:(or, equivalently,
9499:truncated octahedra
9485:is a space-filling
8803:
8333:scaliform honeycomb
8321:trihexagonal tiling
7640:
7609:oblate octahedrille
7538:oblate octahedrille
6091:Honeycomb diagrams
6001:constructed by the
4059:{∞,3,∞}
1591:
348:geometric honeycomb
66:Hypercube honeycomb
18013:
17971:
17935:
17898:
17855:
17812:
17769:
17722:uniform honeycombs
17618:George Olshevsky,
17164:snub square tiling
16602:rhombicuboctahedra
16330:rhombicuboctahedra
16018:
15839:, and creates new
15455:vertex arrangement
15289:
15251:
15215:
15122:
15090:eighth pyramidille
15082:John Horton Conway
15073:phyllic disphenoid
15023:eighth pyramidille
15005:
14951:Fibrifold notation
14940:phyllic disphenoid
14745:rhombicuboctahedra
14713:
14614:vertex arrangement
14610:skew apeirohedrons
14530:
14471:John Horton Conway
14390:rhombicuboctahedra
14329:Fibrifold notation
14310:
14024:rhombicuboctahedra
13207:
13166:
12904:
12864:
12730:
12673:John Horton Conway
12591:Fibrifold notation
12572:
12027:
11987:
11939:
11928:There is a second
11850:
11780:John Horton Conway
11759:rhombicuboctahedra
11699:
11653:Fibrifold notation
11197:
11037:
10223:
10155:
10059:
9963:
9865:
9765:
9741:
9713:fundamental domain
9597:
9568:isosceles triangle
9540:John Horton Conway
9534:uniform honeycombs
9532:. It is one of 28
9479:
9467:, cell-transitive
9423:
9370:Fibrifold notation
9340:isosceles triangle
8973:
8935:
8879:There is a second
8801:
8764:John Horton Conway
8686:
8641:Fibrifold notation
8329:triangular cupolae
8323:planes, using the
7886:
7847:
7808:
7769:
7638:
7607:, and its dual an
7601:John Horton Conway
7519:
7474:Fibrifold notation
7026:
6988:
6906:
6868:
6731:
6690:
6529:
6338:
6297:
6172:
6027:
1589:
880:Colors by letters
606:Rotation subgroup
522:Rotation subgroup
424:uniform honeycombs
403:Related honeycombs
337:John Horton Conway
331:tessellation with
246:
201:Fibrifold notation
18594:Self-dual tilings
18572:
18571:
18174:24-cell honeycomb
17998:
17962:
17926:
17883:
17840:
17797:
17754:
17724:in dimensions 2–9
17647:978-0-471-01003-6
17635:4(1994), 49 - 56.
17604:Regular Polytopes
17594:978-1-56881-220-5
17580:, Heidi Burgiel,
17459:square antiprisms
17395:
17394:
17389:Vertex-transitive
17150:triangular prisms
17142:Euclidean 3-space
17122:
17121:
17117:Vertex-transitive
16924:Uniform honeycomb
16872:Euclidean 3-space
16852:
16851:
16847:Vertex-transitive
16647:Uniform honeycomb
16553:
16552:
16547:Vertex-transitive
16360:triangular prisms
16277:
16276:
16271:Vertex-transitive
16085:
16084:
15986:
15985:
15833:square antiprisms
15767:
15766:
15761:Vertex-transitive
15563:square antiprisms
15501:Related polytopes
15498:
15497:
15451:skew apeirohedron
15445:Related polyhedra
15442:
15441:
15280:
15242:
15193:
15192:
15045:
15044:
15040:Vertex-transitive
14996:
14817:Uniform honeycomb
14757:triangular prisms
14739:Related polytopes
14704:
14601:
14600:
14516:
14515:
14467:cubic honeycomb.
14370:
14369:
14365:Vertex-transitive
14301:
14129:Uniform honeycomb
14073:triangular prisms
14059:Related polytopes
14046:triangular prisms
13963:
13962:
13957:Vertex-transitive
13778:
13777:
13577:
13576:
13571:Vertex-transitive
13249:triangular prisms
13231:Related polytopes
13228:
13227:
13198:skew apeirohedron
13157:
13083:
13082:
12895:
12855:
12801:
12800:
12664:mirrored sphenoid
12632:
12631:
12627:Vertex-transitive
12563:
12535:mirrored sphenoid
12330:Uniform honeycomb
12218:square antiprisms
12196:Related polytopes
12193:
12192:
12018:
11978:
11930:uniform colorings
11921:
11920:
11836:
11835:
11739:
11738:
11734:Vertex-transitive
11690:
11465:Uniform honeycomb
11445:
11444:
11078:
11077:
11072:Vertex-transitive
11028:
10672:scalene triangles
10613:Related polytopes
10610:
10609:
10214:
10146:
10050:
9954:
9856:
9732:
9696:
9695:
9530:vertex-transitive
9495:Euclidean 3-space
9471:
9470:
9461:Vertex-transitive
9414:
9235:Uniform honeycomb
9165:Related polytopes
9162:
9161:
8964:
8926:
8872:
8871:
8768:truncated cubille
8727:
8726:
8722:Vertex-transitive
8677:
8443:Uniform honeycomb
8395:Related polytopes
8317:
8316:
7877:
7838:
7799:
7760:
7718:uniform colorings
7709:
7708:
7564:
7563:
7555:Vertex-transitive
7510:
7085:Uniform honeycomb
7065:
7064:
7017:
6979:
6897:
6859:
6722:
6681:
6520:
6329:
6288:
6163:
6018:
5995:
5994:
5267:
5266:
4287:Related polytopes
4284:
4283:
3976:
3975:
2923:regular polytopes
2919:
2918:
1660:
1659:
1580:triangular tiling
1567:
1566:
1322:{4,4}×t{∞}
848:uniform colorings
842:Uniform colorings
839:
838:
313:Euclidean 3-space
301:cubic cellulation
293:
292:
284:Vertex-transitive
237:
56:Regular honeycomb
16:(Redirected from
18606:
18022:
18020:
18019:
18014:
18012:
18011:
18000:
17999:
17991:
17980:
17978:
17977:
17972:
17970:
17969:
17964:
17963:
17955:
17944:
17942:
17941:
17936:
17934:
17933:
17928:
17927:
17919:
17907:
17905:
17904:
17899:
17897:
17896:
17885:
17884:
17876:
17864:
17862:
17861:
17856:
17854:
17853:
17842:
17841:
17833:
17821:
17819:
17818:
17813:
17811:
17810:
17799:
17798:
17790:
17778:
17776:
17775:
17770:
17768:
17767:
17756:
17755:
17747:
17710:
17703:
17696:
17687:
17686:
17678:
17570:
17565:
17559:
17556:
17550:
17541:
17535:
17532:
17463:octagonal prisms
17456:
17455:
17454:
17450:
17449:
17445:
17444:
17440:
17439:
17435:
17434:
17430:
17429:
17425:
17424:
17420:
17419:
17415:
17414:
17371:
17343:
17334:
17319:
17318:
17317:
17313:
17312:
17308:
17307:
17303:
17302:
17298:
17297:
17293:
17292:
17288:
17287:
17283:
17282:
17278:
17277:
17271:
17270:
17269:
17265:
17264:
17260:
17259:
17255:
17254:
17250:
17249:
17245:
17244:
17240:
17239:
17235:
17234:
17230:
17229:
17194:Convex honeycomb
17182:
17169:It is one of 28
17159:
17108:
17065:
17056:
17041:
17040:
17039:
17035:
17034:
17030:
17029:
17025:
17024:
17020:
17019:
17015:
17014:
17010:
17009:
17005:
17004:
17000:
16999:
16993:
16992:
16991:
16987:
16986:
16982:
16981:
16977:
16976:
16972:
16971:
16967:
16966:
16962:
16961:
16957:
16956:
16952:
16951:
16912:
16899:It is one of 28
16889:
16876:octagonal prisms
16838:
16796:
16787:
16772:
16771:
16770:
16766:
16765:
16761:
16760:
16756:
16755:
16751:
16750:
16746:
16745:
16741:
16740:
16736:
16735:
16731:
16730:
16724:
16723:
16722:
16718:
16717:
16713:
16712:
16708:
16707:
16703:
16702:
16698:
16697:
16693:
16692:
16688:
16687:
16683:
16682:
16664:tr{4,4}×{∞} or t
16635:
16599:
16598:
16597:
16593:
16592:
16588:
16587:
16583:
16582:
16578:
16577:
16573:
16572:
16568:
16567:
16538:
16509:
16479:
16470:
16451:
16450:
16449:
16445:
16444:
16440:
16439:
16435:
16434:
16430:
16429:
16425:
16424:
16420:
16419:
16411:Coxeter diagrams
16390:Convex honeycomb
16378:
16327:
16326:
16325:
16321:
16320:
16316:
16315:
16311:
16310:
16306:
16305:
16301:
16300:
16296:
16295:
16262:
16240:
16212:
16203:
16194:
16185:
16166:
16165:
16164:
16160:
16159:
16155:
16154:
16150:
16149:
16145:
16144:
16140:
16139:
16135:
16134:
16126:Coxeter diagrams
16105:Convex honeycomb
16093:
16081:
16074:
16067:
16060:
16051:
16044:
16037:
16028:
16021:
16017:
16011:
15934:
15922:
15921:
15920:
15916:
15915:
15911:
15910:
15906:
15905:
15901:
15900:
15896:
15895:
15891:
15890:
15851:
15837:octagonal prisms
15822:
15821:
15820:
15816:
15815:
15811:
15810:
15806:
15805:
15801:
15800:
15796:
15795:
15791:
15790:
15732:
15727:
15699:
15690:
15681:
15666:
15665:
15664:
15660:
15659:
15655:
15654:
15650:
15649:
15645:
15644:
15640:
15639:
15635:
15634:
15605:Convex honeycomb
15593:
15580:
15550:
15539:
15515:hexagonal prisms
15511:octagonal prisms
15494:
15487:
15478:
15469:
15460:
15459:
15438:
15431:
15417:
15416:
15415:
15411:
15410:
15406:
15405:
15398:
15397:
15396:
15392:
15391:
15387:
15386:
15382:
15381:
15377:
15376:
15372:
15371:
15367:
15366:
15352:
15345:
15319:
15312:
15298:
15296:
15295:
15290:
15288:
15287:
15282:
15281:
15273:
15260:
15258:
15257:
15252:
15250:
15249:
15244:
15243:
15235:
15218:
15214:
15210:octagonal prisms
15189:
15182:
15175:
15163:
15156:
15149:
15125:
15121:
15106:
15100:
15069:octagonal prisms
15031:
15014:
15012:
15011:
15006:
15004:
15003:
14998:
14997:
14989:
14963:
14955:Coxeter notation
14937:
14902:
14893:
14878:
14877:
14876:
14872:
14871:
14867:
14866:
14862:
14861:
14857:
14856:
14852:
14851:
14847:
14846:
14805:
14792:
14781:
14734:
14722:
14720:
14719:
14714:
14712:
14711:
14706:
14705:
14697:
14686:
14685:
14684:
14680:
14679:
14675:
14674:
14670:
14669:
14665:
14664:
14660:
14659:
14655:
14654:
14638:The dual to the
14629:
14624:
14597:
14590:
14583:
14571:
14564:
14557:
14533:
14529:
14512:
14505:
14498:
14491:
14484:
14483:
14458:
14457:
14456:
14452:
14451:
14447:
14446:
14442:
14441:
14437:
14436:
14432:
14431:
14427:
14426:
14398:octagonal prisms
14356:
14336:
14319:
14317:
14316:
14311:
14309:
14308:
14303:
14302:
14294:
14267:
14232:
14223:
14214:
14205:
14190:
14189:
14188:
14184:
14183:
14179:
14178:
14174:
14173:
14169:
14168:
14164:
14163:
14159:
14158:
14150:Coxeter diagrams
14117:
14104:
14093:
14021:
14020:
14019:
14015:
14014:
14010:
14009:
14005:
14004:
14000:
13999:
13995:
13994:
13990:
13989:
13948:
13926:
13896:
13887:
13878:
13859:
13858:
13857:
13853:
13852:
13848:
13847:
13843:
13842:
13838:
13837:
13833:
13832:
13828:
13827:
13819:Coxeter diagrams
13798:Convex honeycomb
13786:
13774:
13773:
13772:
13768:
13767:
13763:
13762:
13758:
13757:
13753:
13752:
13748:
13747:
13743:
13742:
13736:
13729:
13728:
13727:
13723:
13722:
13718:
13717:
13713:
13712:
13708:
13707:
13703:
13702:
13698:
13697:
13691:
13684:
13683:
13676:
13675:
13674:
13670:
13669:
13665:
13664:
13660:
13659:
13655:
13654:
13650:
13649:
13645:
13644:
13638:
13637:
13636:
13632:
13631:
13627:
13626:
13622:
13621:
13617:
13616:
13610:Coxeter diagrams
13562:
13555:
13554:
13553:
13549:
13548:
13544:
13543:
13539:
13538:
13534:
13533:
13529:
13528:
13524:
13523:
13502:
13497:
13467:
13458:
13449:
13434:
13433:
13432:
13428:
13427:
13423:
13422:
13418:
13417:
13413:
13412:
13408:
13407:
13403:
13402:
13396:
13395:
13394:
13390:
13389:
13385:
13384:
13380:
13379:
13375:
13374:
13368:
13367:
13366:
13362:
13361:
13357:
13356:
13352:
13351:
13347:
13346:
13342:
13341:
13337:
13336:
13328:Coxeter diagrams
13309:Convex honeycomb
13297:
13284:
13273:
13241:hexagonal prisms
13224:
13217:
13210:
13206:
13187:
13175:
13173:
13172:
13167:
13165:
13164:
13159:
13158:
13150:
13139:
13138:
13137:
13133:
13132:
13128:
13127:
13123:
13122:
13118:
13117:
13113:
13112:
13108:
13107:
13090:The dual of the
13062:
13055:
13041:
13040:
13039:
13035:
13034:
13030:
13029:
13025:
13024:
13020:
13019:
13012:
13011:
13010:
13006:
13005:
13001:
13000:
12996:
12995:
12991:
12990:
12986:
12985:
12981:
12980:
12966:
12959:
12933:
12926:
12913:
12911:
12910:
12905:
12903:
12902:
12897:
12896:
12888:
12873:
12871:
12870:
12865:
12863:
12862:
12857:
12856:
12848:
12819:
12797:
12790:
12783:
12771:
12764:
12757:
12733:
12729:
12714:
12697:
12691:
12618:
12598:
12581:
12579:
12578:
12573:
12571:
12570:
12565:
12564:
12556:
12532:
12527:
12492:
12483:
12474:
12459:
12458:
12457:
12453:
12452:
12448:
12447:
12443:
12442:
12438:
12437:
12433:
12432:
12428:
12427:
12421:
12420:
12419:
12415:
12414:
12410:
12409:
12405:
12404:
12400:
12399:
12393:
12392:
12391:
12387:
12386:
12382:
12381:
12377:
12376:
12372:
12371:
12367:
12366:
12362:
12361:
12318:
12309:
12297:
12296:
12295:
12291:
12290:
12286:
12285:
12281:
12280:
12276:
12275:
12271:
12270:
12266:
12265:
12245:The dual of the
12234:triangular prism
12172:
12165:
12151:
12144:
12132:
12131:
12130:
12126:
12125:
12121:
12120:
12116:
12115:
12111:
12110:
12103:
12102:
12101:
12097:
12096:
12092:
12091:
12087:
12086:
12082:
12081:
12077:
12076:
12072:
12071:
12056:
12049:
12036:
12034:
12033:
12028:
12026:
12025:
12020:
12019:
12011:
11996:
11994:
11993:
11988:
11986:
11985:
11980:
11979:
11971:
11942:
11917:
11910:
11903:
11891:
11884:
11877:
11853:
11849:
11826:
11819:
11812:
11803:
11798:
11725:
11708:
11706:
11705:
11700:
11698:
11697:
11692:
11691:
11683:
11660:
11639:
11627:
11618:
11609:
11594:
11593:
11592:
11588:
11587:
11583:
11582:
11578:
11577:
11573:
11572:
11568:
11567:
11563:
11562:
11556:
11555:
11554:
11550:
11549:
11545:
11544:
11540:
11539:
11535:
11534:
11528:
11527:
11526:
11522:
11521:
11517:
11516:
11512:
11511:
11507:
11506:
11502:
11501:
11497:
11496:
11453:
11419:
11418:
11417:
11413:
11412:
11408:
11407:
11403:
11402:
11398:
11397:
11390:
11389:
11388:
11384:
11383:
11379:
11378:
11371:
11370:
11369:
11365:
11364:
11360:
11359:
11355:
11354:
11350:
11349:
11342:
11341:
11340:
11336:
11335:
11331:
11330:
11326:
11325:
11321:
11320:
11316:
11315:
11311:
11310:
11303:
11302:
11301:
11297:
11296:
11292:
11291:
11232:
11225:
11218:
11211:
11200:
11196:
11186:
11185:
11184:
11180:
11179:
11175:
11174:
11170:
11169:
11165:
11164:
11158:
11157:
11156:
11152:
11151:
11147:
11146:
11142:
11141:
11137:
11136:
11130:
11129:
11128:
11124:
11123:
11119:
11118:
11114:
11113:
11109:
11108:
11104:
11103:
11099:
11098:
11091:Coxeter diagrams
11063:
11046:
11044:
11043:
11038:
11036:
11035:
11030:
11029:
11021:
11001:
10978:
10969:
10954:
10953:
10952:
10948:
10947:
10943:
10942:
10938:
10937:
10933:
10932:
10928:
10927:
10923:
10922:
10916:
10915:
10914:
10910:
10909:
10905:
10904:
10900:
10899:
10895:
10894:
10888:
10887:
10886:
10882:
10881:
10877:
10876:
10872:
10871:
10867:
10866:
10862:
10861:
10857:
10856:
10850:
10849:
10848:
10844:
10843:
10839:
10838:
10834:
10833:
10829:
10828:
10822:
10821:
10820:
10816:
10815:
10811:
10810:
10806:
10805:
10801:
10800:
10796:
10795:
10791:
10790:
10784:
10783:
10782:
10778:
10777:
10773:
10772:
10768:
10767:
10763:
10762:
10756:
10755:
10754:
10750:
10749:
10745:
10744:
10740:
10739:
10735:
10734:
10730:
10729:
10725:
10724:
10716:Coxeter diagrams
10695:Convex honeycomb
10683:
10623:hexagonal prisms
10606:
10599:
10592:
10585:
10578:
10533:
10526:
10519:
10512:
10505:
10491:
10485:
10476:
10470:
10464:
10458:
10449:
10443:
10437:
10428:
10422:
10413:
10397:
10396:
10395:
10391:
10390:
10386:
10385:
10378:
10377:
10376:
10372:
10371:
10367:
10366:
10362:
10361:
10357:
10356:
10349:
10348:
10347:
10343:
10342:
10338:
10337:
10333:
10332:
10328:
10327:
10320:
10319:
10318:
10314:
10313:
10309:
10308:
10304:
10303:
10299:
10298:
10294:
10293:
10289:
10288:
10281:
10280:
10279:
10275:
10274:
10270:
10269:
10255:
10254:
10253:
10249:
10248:
10244:
10243:
10232:
10230:
10229:
10224:
10222:
10221:
10216:
10215:
10207:
10195:
10194:
10193:
10189:
10188:
10184:
10183:
10179:
10178:
10174:
10173:
10164:
10162:
10161:
10156:
10154:
10153:
10148:
10147:
10139:
10127:
10126:
10125:
10121:
10120:
10116:
10115:
10111:
10110:
10106:
10105:
10099:
10098:
10097:
10093:
10092:
10088:
10087:
10083:
10082:
10078:
10077:
10068:
10066:
10065:
10060:
10058:
10057:
10052:
10051:
10043:
10031:
10030:
10029:
10025:
10024:
10020:
10019:
10013:
10012:
10011:
10007:
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10002:
10001:
9997:
9996:
9992:
9991:
9987:
9986:
9982:
9981:
9972:
9970:
9969:
9964:
9962:
9961:
9956:
9955:
9947:
9935:
9934:
9933:
9929:
9928:
9924:
9923:
9917:
9916:
9915:
9911:
9910:
9906:
9905:
9901:
9900:
9896:
9895:
9891:
9890:
9886:
9885:
9874:
9872:
9871:
9866:
9864:
9863:
9858:
9857:
9849:
9807:
9800:
9793:
9786:
9779:
9768:
9764:
9750:
9748:
9747:
9742:
9740:
9739:
9734:
9733:
9725:
9692:
9685:
9678:
9671:
9664:
9652:
9645:
9638:
9631:
9624:
9600:
9596:
9554:, also called a
9452:
9432:
9430:
9429:
9424:
9422:
9421:
9416:
9415:
9407:
9382:
9374:Coxeter notation
9356:
9313:
9298:
9297:
9296:
9292:
9291:
9287:
9286:
9282:
9281:
9277:
9276:
9272:
9271:
9267:
9266:
9226:
9220:
9208:
9195:
9184:
9158:
9151:
9137:
9136:
9135:
9131:
9130:
9126:
9125:
9121:
9120:
9116:
9115:
9111:
9110:
9106:
9105:
9098:
9097:
9096:
9092:
9091:
9087:
9086:
9082:
9081:
9077:
9076:
9072:
9071:
9067:
9066:
9060:
9059:
9058:
9054:
9053:
9049:
9048:
9044:
9043:
9039:
9038:
9024:
9017:
9004:
8997:
8982:
8980:
8979:
8974:
8972:
8971:
8966:
8965:
8957:
8944:
8942:
8941:
8936:
8934:
8933:
8928:
8927:
8919:
8890:
8881:uniform coloring
8868:
8861:
8854:
8842:
8835:
8828:
8804:
8800:
8786:
8781:
8713:
8695:
8693:
8692:
8687:
8685:
8684:
8679:
8678:
8670:
8648:
8626:
8596:
8587:
8572:
8571:
8570:
8566:
8565:
8561:
8560:
8556:
8555:
8551:
8550:
8546:
8545:
8541:
8540:
8534:
8533:
8532:
8528:
8527:
8523:
8522:
8518:
8517:
8513:
8512:
8506:
8505:
8504:
8500:
8499:
8495:
8494:
8490:
8489:
8485:
8484:
8480:
8479:
8475:
8474:
8466:Coxeter diagrams
8431:
8418:
8405:square bifrustum
8389:
8379:coxeter notation
8372:
8371:
8370:
8366:
8365:
8361:
8360:
8356:
8355:
8351:
8350:
8346:
8345:
8341:
8340:
8260:
8253:
8246:
8239:
8225:
8224:
8223:
8219:
8218:
8214:
8213:
8209:
8208:
8204:
8203:
8196:
8195:
8194:
8190:
8189:
8185:
8184:
8180:
8179:
8175:
8174:
8167:
8166:
8165:
8161:
8160:
8156:
8155:
8151:
8150:
8146:
8145:
8136:
8135:
8134:
8130:
8129:
8125:
8124:
8120:
8119:
8115:
8114:
8110:
8109:
8105:
8104:
8097:
8096:
8095:
8091:
8090:
8086:
8085:
8081:
8080:
8076:
8075:
8071:
8070:
8066:
8065:
8058:
8057:
8056:
8052:
8051:
8047:
8046:
8042:
8041:
8037:
8036:
8032:
8031:
8027:
8026:
8019:
8018:
8017:
8013:
8012:
8008:
8007:
8003:
8002:
7998:
7997:
7993:
7992:
7988:
7987:
7971:
7964:
7957:
7950:
7935:
7926:
7917:
7908:
7895:
7893:
7892:
7887:
7885:
7884:
7879:
7878:
7870:
7856:
7854:
7853:
7848:
7846:
7845:
7840:
7839:
7831:
7817:
7815:
7814:
7809:
7807:
7806:
7801:
7800:
7792:
7778:
7776:
7775:
7770:
7768:
7767:
7762:
7761:
7753:
7735:
7705:
7698:
7691:
7679:
7672:
7665:
7641:
7637:
7623:
7618:
7546:
7528:
7526:
7525:
7520:
7518:
7517:
7512:
7511:
7503:
7481:
7460:
7430:
7421:
7406:
7405:
7404:
7400:
7399:
7395:
7394:
7390:
7389:
7385:
7384:
7380:
7379:
7375:
7374:
7368:
7367:
7366:
7362:
7361:
7357:
7356:
7352:
7351:
7347:
7346:
7340:
7339:
7338:
7334:
7333:
7329:
7328:
7324:
7323:
7319:
7318:
7312:
7311:
7310:
7306:
7305:
7301:
7300:
7296:
7295:
7291:
7290:
7284:
7283:
7282:
7278:
7277:
7273:
7272:
7268:
7267:
7263:
7262:
7258:
7257:
7253:
7252:
7246:
7245:
7244:
7240:
7239:
7235:
7234:
7230:
7229:
7225:
7224:
7218:
7217:
7216:
7212:
7211:
7207:
7206:
7202:
7201:
7197:
7196:
7192:
7191:
7187:
7186:
7180:
7179:
7178:
7174:
7173:
7169:
7168:
7164:
7163:
7159:
7158:
7152:
7151:
7150:
7146:
7145:
7141:
7140:
7136:
7135:
7131:
7130:
7126:
7125:
7121:
7120:
7112:Coxeter diagrams
7073:
7055:
7054:
7053:
7049:
7048:
7044:
7043:
7035:
7033:
7032:
7027:
7025:
7024:
7019:
7018:
7010:
6997:
6995:
6994:
6989:
6987:
6986:
6981:
6980:
6972:
6949:
6935:
6934:
6933:
6929:
6928:
6924:
6923:
6915:
6913:
6912:
6907:
6905:
6904:
6899:
6898:
6890:
6877:
6875:
6874:
6869:
6867:
6866:
6861:
6860:
6852:
6839:
6838:
6837:
6833:
6832:
6828:
6827:
6820:
6819:
6818:
6814:
6813:
6809:
6808:
6796:
6783:
6769:
6768:
6767:
6763:
6762:
6758:
6757:
6753:
6752:
6748:
6747:
6740:
6738:
6737:
6732:
6730:
6729:
6724:
6723:
6715:
6699:
6697:
6696:
6691:
6689:
6688:
6683:
6682:
6674:
6662:
6661:
6660:
6656:
6655:
6651:
6650:
6646:
6645:
6641:
6640:
6636:
6635:
6631:
6630:
6623:
6622:
6621:
6617:
6616:
6612:
6611:
6607:
6606:
6602:
6601:
6589:
6575:
6561:
6560:
6559:
6555:
6554:
6550:
6549:
6538:
6536:
6535:
6530:
6528:
6527:
6522:
6521:
6513:
6501:
6500:
6499:
6495:
6494:
6490:
6489:
6485:
6484:
6480:
6479:
6475:
6474:
6470:
6469:
6462:
6461:
6460:
6456:
6455:
6451:
6450:
6438:
6424:
6410:
6409:
6408:
6404:
6403:
6399:
6398:
6394:
6393:
6389:
6388:
6376:
6375:
6374:
6370:
6369:
6365:
6364:
6360:
6359:
6355:
6354:
6347:
6345:
6344:
6339:
6337:
6336:
6331:
6330:
6322:
6306:
6304:
6303:
6298:
6296:
6295:
6290:
6289:
6281:
6269:
6268:
6267:
6263:
6262:
6258:
6257:
6253:
6252:
6248:
6247:
6240:
6239:
6238:
6234:
6233:
6229:
6228:
6224:
6223:
6219:
6218:
6206:
6192:
6181:
6179:
6178:
6173:
6171:
6170:
6165:
6164:
6156:
6144:
6143:
6142:
6138:
6137:
6133:
6132:
6128:
6127:
6123:
6122:
6113:
6099:
6047:
6046:
6036:
6034:
6033:
6028:
6026:
6025:
6020:
6019:
6011:
5985:
5984:
5983:
5979:
5978:
5974:
5973:
5969:
5968:
5964:
5963:
5952:
5951:
5950:
5946:
5945:
5941:
5940:
5936:
5935:
5931:
5930:
5919:
5918:
5917:
5913:
5912:
5908:
5907:
5903:
5902:
5898:
5897:
5886:
5885:
5884:
5880:
5879:
5875:
5874:
5870:
5869:
5865:
5864:
5853:
5852:
5851:
5847:
5846:
5842:
5841:
5837:
5836:
5832:
5831:
5820:
5819:
5818:
5814:
5813:
5809:
5808:
5804:
5803:
5799:
5798:
5787:
5786:
5785:
5781:
5780:
5776:
5775:
5771:
5770:
5766:
5765:
5754:
5753:
5752:
5748:
5747:
5743:
5742:
5738:
5737:
5733:
5732:
5716:
5703:
5702:
5701:
5697:
5696:
5692:
5691:
5687:
5686:
5682:
5681:
5670:
5669:
5668:
5664:
5663:
5659:
5658:
5654:
5653:
5649:
5648:
5638:
5637:
5636:
5632:
5631:
5627:
5626:
5622:
5621:
5617:
5616:
5609:
5608:
5607:
5603:
5602:
5598:
5597:
5593:
5592:
5588:
5587:
5569:
5556:
5555:
5554:
5550:
5549:
5545:
5544:
5540:
5539:
5535:
5534:
5523:
5522:
5521:
5517:
5516:
5512:
5511:
5507:
5506:
5502:
5501:
5490:
5489:
5488:
5484:
5483:
5479:
5478:
5474:
5473:
5469:
5468:
5457:
5456:
5455:
5451:
5450:
5446:
5445:
5441:
5440:
5436:
5435:
5425:
5424:
5423:
5419:
5418:
5414:
5413:
5409:
5408:
5404:
5403:
5399:
5398:
5394:
5393:
5386:
5385:
5384:
5380:
5379:
5375:
5374:
5370:
5369:
5365:
5364:
5347:
5304:
5303:
5296:
5295:
5294:
5290:
5289:
5285:
5284:
5280:
5279:
5275:
5274:
5257:
5256:
5255:
5251:
5250:
5246:
5245:
5234:
5233:
5232:
5228:
5227:
5223:
5222:
5211:
5210:
5209:
5205:
5204:
5200:
5199:
5188:
5187:
5186:
5182:
5181:
5177:
5176:
5160:
5146:
5145:
5144:
5140:
5139:
5135:
5134:
5124:
5123:
5122:
5118:
5117:
5113:
5112:
5105:
5104:
5103:
5099:
5098:
5094:
5093:
5075:
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5059:
5055:
5054:
5050:
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5039:
5038:
5037:
5033:
5032:
5028:
5027:
5011:
4998:
4997:
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4992:
4991:
4987:
4986:
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4981:
4977:
4976:
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4966:
4955:
4954:
4953:
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4934:
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4924:
4923:
4912:
4911:
4910:
4906:
4905:
4901:
4900:
4896:
4895:
4891:
4890:
4886:
4885:
4881:
4880:
4869:
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4867:
4863:
4862:
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4852:
4848:
4847:
4843:
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4821:
4820:
4816:
4815:
4811:
4810:
4806:
4805:
4798:
4797:
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4786:
4782:
4781:
4777:
4776:
4772:
4771:
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4736:
4735:
4734:
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4715:
4714:
4710:
4709:
4705:
4704:
4693:
4692:
4691:
4687:
4686:
4682:
4681:
4677:
4676:
4672:
4671:
4667:
4666:
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4661:
4649:
4648:
4647:
4643:
4642:
4638:
4637:
4633:
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4606:
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4599:
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4589:
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4563:
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4503:
4499:
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4493:
4489:
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4472:
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3448:
3447:
3443:
3442:
3438:
3437:
3433:
3432:
3428:
3427:
3423:
3422:
3416:
3415:
3414:
3410:
3409:
3405:
3404:
3400:
3399:
3395:
3394:
3390:
3389:
3385:
3384:
3373:
3372:
3371:
3367:
3366:
3362:
3361:
3357:
3356:
3352:
3351:
3347:
3346:
3342:
3341:
3330:
3329:
3328:
3324:
3323:
3319:
3318:
3314:
3313:
3309:
3308:
3304:
3303:
3299:
3298:
3292:
3291:
3290:
3286:
3285:
3281:
3280:
3276:
3275:
3271:
3270:
3264:
3263:
3262:
3258:
3257:
3253:
3252:
3248:
3247:
3243:
3242:
3238:
3237:
3233:
3232:
3221:
3220:
3219:
3215:
3214:
3210:
3209:
3205:
3204:
3200:
3199:
3195:
3194:
3190:
3189:
3178:
3177:
3176:
3172:
3171:
3167:
3166:
3162:
3161:
3157:
3156:
3152:
3151:
3147:
3146:
3142:
3141:
3135:
3134:
3133:
3129:
3128:
3124:
3123:
3119:
3118:
3114:
3113:
3107:
3106:
3105:
3101:
3100:
3096:
3095:
3091:
3090:
3086:
3085:
3081:
3080:
3076:
3075:
3064:
3063:
3062:
3058:
3057:
3053:
3052:
3048:
3047:
3043:
3042:
3038:
3037:
3033:
3032:
3021:
3020:
3019:
3015:
3014:
3010:
3009:
3005:
3004:
3000:
2999:
2995:
2994:
2990:
2989:
2935:
2934:
2915:
2914:
2913:
2909:
2908:
2904:
2903:
2899:
2898:
2894:
2893:
2883:
2876:
2875:
2874:
2870:
2869:
2865:
2864:
2860:
2859:
2855:
2854:
2844:
2837:
2836:
2835:
2831:
2830:
2826:
2825:
2821:
2820:
2816:
2815:
2805:
2798:
2797:
2796:
2792:
2791:
2787:
2786:
2782:
2781:
2777:
2776:
2766:
2759:
2758:
2757:
2753:
2752:
2748:
2747:
2743:
2742:
2738:
2737:
2727:
2720:
2719:
2718:
2714:
2713:
2709:
2708:
2704:
2703:
2699:
2698:
2688:
2681:
2680:
2679:
2675:
2674:
2670:
2669:
2665:
2664:
2660:
2659:
2649:
2637:
2630:
2623:
2616:
2609:
2602:
2595:
2583:
2582:
2581:
2577:
2576:
2572:
2571:
2567:
2566:
2562:
2561:
2557:
2556:
2552:
2551:
2547:
2546:
2540:
2539:
2538:
2534:
2533:
2529:
2528:
2524:
2523:
2519:
2518:
2514:
2513:
2509:
2508:
2504:
2503:
2497:
2496:
2495:
2491:
2490:
2486:
2485:
2481:
2480:
2476:
2475:
2469:
2468:
2467:
2463:
2462:
2458:
2457:
2453:
2452:
2448:
2447:
2443:
2442:
2438:
2437:
2425:
2424:
2423:
2419:
2418:
2414:
2413:
2409:
2408:
2404:
2403:
2399:
2398:
2394:
2393:
2389:
2388:
2382:
2381:
2380:
2376:
2375:
2371:
2370:
2366:
2365:
2361:
2360:
2356:
2355:
2351:
2350:
2346:
2345:
2339:
2338:
2337:
2333:
2332:
2328:
2327:
2323:
2322:
2318:
2317:
2311:
2310:
2309:
2305:
2304:
2300:
2299:
2295:
2294:
2290:
2289:
2285:
2284:
2280:
2279:
2268:
2267:
2266:
2262:
2261:
2257:
2256:
2252:
2251:
2247:
2246:
2240:
2239:
2238:
2234:
2233:
2229:
2228:
2224:
2223:
2219:
2218:
2214:
2213:
2209:
2208:
2197:
2196:
2195:
2191:
2190:
2186:
2185:
2181:
2180:
2176:
2175:
2171:
2170:
2166:
2165:
2159:
2158:
2157:
2153:
2152:
2148:
2147:
2143:
2142:
2138:
2137:
2133:
2132:
2128:
2127:
2121:
2120:
2119:
2115:
2114:
2110:
2109:
2105:
2104:
2100:
2099:
2093:
2092:
2091:
2087:
2086:
2082:
2081:
2077:
2076:
2072:
2071:
2067:
2066:
2062:
2061:
2050:
2049:
2048:
2044:
2043:
2039:
2038:
2034:
2033:
2029:
2028:
2022:
2021:
2020:
2016:
2015:
2011:
2010:
2006:
2005:
2001:
2000:
1996:
1995:
1991:
1990:
1979:
1978:
1977:
1973:
1972:
1968:
1967:
1963:
1962:
1958:
1957:
1953:
1952:
1948:
1947:
1943:
1942:
1936:
1935:
1934:
1930:
1929:
1925:
1924:
1920:
1919:
1915:
1914:
1910:
1909:
1905:
1904:
1900:
1899:
1893:
1892:
1891:
1887:
1886:
1882:
1881:
1877:
1876:
1872:
1871:
1865:
1864:
1863:
1859:
1858:
1854:
1853:
1849:
1848:
1844:
1843:
1839:
1838:
1834:
1833:
1822:
1821:
1820:
1816:
1815:
1811:
1810:
1806:
1805:
1801:
1800:
1794:
1793:
1792:
1788:
1787:
1783:
1782:
1778:
1777:
1773:
1772:
1768:
1767:
1763:
1762:
1703:
1702:
1688:hyperbolic space
1656:
1649:
1642:
1630:
1623:
1616:
1592:
1588:
1560:
1550:
1549:
1548:
1544:
1543:
1539:
1538:
1534:
1533:
1529:
1528:
1524:
1523:
1519:
1518:
1512:
1511:
1510:
1506:
1505:
1501:
1500:
1496:
1495:
1491:
1490:
1486:
1485:
1481:
1480:
1476:
1475:
1460:
1450:
1449:
1448:
1444:
1443:
1439:
1438:
1434:
1433:
1429:
1428:
1424:
1423:
1419:
1418:
1414:
1413:
1399:
1392:{4,4}×{∞}
1385:
1384:
1383:
1379:
1378:
1374:
1373:
1369:
1368:
1364:
1363:
1359:
1358:
1354:
1353:
1349:
1348:
1344:
1343:
1329:
1319:
1318:
1317:
1313:
1312:
1308:
1307:
1303:
1302:
1298:
1297:
1293:
1292:
1288:
1287:
1283:
1282:
1275:
1274:
1273:
1269:
1268:
1264:
1263:
1259:
1258:
1254:
1253:
1249:
1248:
1244:
1243:
1239:
1238:
1234:
1233:
1210:
1209:
1208:
1204:
1203:
1199:
1198:
1190:
1177:
1163:
1162:
1161:
1157:
1156:
1152:
1151:
1147:
1146:
1142:
1141:
1137:
1136:
1132:
1131:
1123:
1111:
1101:
1100:
1099:
1095:
1094:
1090:
1089:
1085:
1084:
1080:
1079:
1075:
1074:
1070:
1069:
1063:
1062:
1061:
1057:
1056:
1052:
1051:
1047:
1046:
1042:
1041:
1033:
1020:
1010:
1009:
1008:
1004:
1003:
999:
998:
994:
993:
989:
988:
984:
983:
979:
978:
972:
971:
970:
966:
965:
961:
960:
956:
955:
951:
950:
946:
945:
941:
940:
936:
935:
929:
928:
927:
923:
922:
918:
917:
913:
912:
908:
907:
903:
902:
898:
897:
889:
857:Coxeter notation
853:
852:
835:
834:
833:
829:
828:
824:
823:
819:
818:
814:
813:
809:
808:
804:
803:
793:
792:
791:
787:
786:
782:
781:
777:
776:
772:
771:
767:
766:
762:
761:
757:
756:
752:
751:
744:
743:
742:
738:
737:
733:
732:
728:
727:
723:
722:
718:
717:
713:
712:
708:
707:
703:
702:
698:
697:
693:
692:
641:Coxeter notation
632:
597:
590:
583:
576:
569:
441:
440:
422:It is one of 28
413:Schläfli symbols
393:uniform polytope
275:
255:
253:
252:
247:
245:
244:
239:
238:
230:
208:
187:
162:
147:
146:
145:
141:
140:
136:
135:
131:
130:
126:
125:
121:
120:
116:
115:
47:
42:
33:Cubic honeycomb
30:
21:
18614:
18613:
18609:
18608:
18607:
18605:
18604:
18603:
18574:
18573:
18567:
18560:
18553:
18545:
18544:
18533:
18532:
18521:
18520:
18509:
18486:
18485:
18478:
18477:
18470:
18469:
18462:
18447:
18446:
18439:
18438:
18431:
18430:
18423:
18407:
18400:
18393:
18386:
18385:
18377:
18376:
18367:
18366:
18357:
18340:
18333:
18325:
18324:
18315:
18314:
18305:
18304:
18295:
18278:
18270:
18269:
18260:
18259:
18250:
18249:
18240:
18221:
18220:
18211:
18210:
18201:
18200:
18191:
18169:
18168:
18159:
18158:
18149:
18148:
18139:
18120:
18119:
18110:
18109:
18100:
18099:
18090:
18068:
18067:
18058:
18057:
18048:
18047:
18038:
18001:
17990:
17989:
17988:
17986:
17983:
17982:
17965:
17954:
17953:
17952:
17950:
17947:
17946:
17929:
17918:
17917:
17916:
17914:
17911:
17910:
17886:
17875:
17874:
17873:
17871:
17868:
17867:
17843:
17832:
17831:
17830:
17828:
17825:
17824:
17800:
17789:
17788:
17787:
17785:
17782:
17781:
17757:
17746:
17745:
17744:
17742:
17739:
17738:
17725:
17714:
17629:Branko Grünbaum
17600:Coxeter, H.S.M.
17574:
17573:
17566:
17562:
17557:
17553:
17542:
17538:
17533:
17529:
17524:
17511:Snub (geometry)
17486:
17480:
17452:
17447:
17442:
17437:
17432:
17427:
17422:
17417:
17412:
17410:
17407:Coxeter diagram
17355:
17335:
17315:
17310:
17305:
17300:
17295:
17290:
17285:
17280:
17275:
17273:
17272:
17267:
17262:
17257:
17252:
17247:
17242:
17237:
17232:
17227:
17225:
17214:
17210:
17208:
17201:Schläfli symbol
17180:
17175:
17102:
17091:
17077:
17057:
17037:
17032:
17027:
17022:
17017:
17012:
17007:
17002:
16997:
16995:
16994:
16989:
16984:
16979:
16974:
16969:
16964:
16959:
16954:
16949:
16947:
16936:
16931:Schläfli symbol
16910:
16905:
16832:
16808:
16788:
16768:
16763:
16758:
16753:
16748:
16743:
16738:
16733:
16728:
16726:
16725:
16720:
16715:
16710:
16705:
16700:
16695:
16690:
16685:
16680:
16678:
16667:
16663:
16661:
16658:t{4,4}×{∞} or t
16654:Schläfli symbol
16633:
16628:
16624:
16609:
16595:
16590:
16585:
16580:
16575:
16570:
16565:
16563:
16561:Coxeter diagram
16510:
16491:
16471:
16463:
16447:
16442:
16437:
16432:
16427:
16422:
16417:
16415:
16404:
16397:Schläfli symbol
16376:
16371:
16367:
16358:symmetry), and
16356:
16343:, two kinds of
16337:
16323:
16318:
16313:
16308:
16303:
16298:
16293:
16291:
16289:Coxeter diagram
16224:
16204:
16195:
16186:
16178:
16162:
16157:
16152:
16147:
16142:
16137:
16132:
16130:
16119:
16112:Schläfli symbol
16091:
16086:
16029:
15981:Cell-transitive
15949:
15945:
15918:
15913:
15908:
15903:
15898:
15893:
15888:
15886:
15882:Coxeter diagram
15875:
15868:Schläfli symbol
15849:
15818:
15813:
15808:
15803:
15798:
15793:
15788:
15786:
15783:Coxeter diagram
15711:
15691:
15682:
15662:
15657:
15652:
15647:
15642:
15637:
15632:
15630:
15626:Coxeter diagram
15619:
15612:Schläfli symbol
15591:
15586:
15581:
15551:
15540:
15526:
15503:
15473:
15464:
15447:
15413:
15408:
15403:
15401:
15394:
15389:
15384:
15379:
15374:
15369:
15364:
15362:
15358:Coxeter diagram
15317:
15310:
15283:
15272:
15271:
15270:
15268:
15265:
15264:
15245:
15234:
15233:
15232:
15230:
15227:
15226:
15202:Coxeter diagram
15198:
15113:
15088:, and its dual
15025:
14999:
14988:
14987:
14986:
14984:
14981:
14980:
14968:
14966:
14961:
14953:
14949:
14938:
14919:
14914:
14894:
14874:
14869:
14864:
14859:
14854:
14849:
14844:
14842:
14838:Coxeter diagram
14831:
14824:Schläfli symbol
14803:
14798:
14793:
14782:
14764:
14741:
14723:Coxeter group.
14707:
14696:
14695:
14694:
14692:
14689:
14688:
14682:
14677:
14672:
14667:
14662:
14657:
14652:
14650:
14648:Coxeter diagram
14636:
14606:
14521:
14477:, and its dual
14454:
14449:
14444:
14439:
14434:
14429:
14424:
14422:
14419:Coxeter diagram
14394:truncated cubes
14350:
14338:
14334:
14327:
14304:
14293:
14292:
14291:
14289:
14286:
14285:
14268:
14249:
14244:
14224:
14215:
14206:
14186:
14181:
14176:
14171:
14166:
14161:
14156:
14154:
14143:
14136:Schläfli symbol
14115:
14110:
14105:
14094:
14084:square pyramids
14080:
14061:
14053:
14044:symmetry), and
14042:
14031:
14017:
14012:
14007:
14002:
13997:
13992:
13987:
13985:
13983:Coxeter diagram
13908:
13888:
13879:
13871:
13855:
13850:
13845:
13840:
13835:
13830:
13825:
13823:
13812:
13805:Schläfli symbol
13784:
13779:
13770:
13765:
13760:
13755:
13750:
13745:
13740:
13738:
13737:
13725:
13720:
13715:
13710:
13705:
13700:
13695:
13693:
13692:
13672:
13667:
13662:
13657:
13652:
13647:
13642:
13640:
13634:
13629:
13624:
13619:
13614:
13612:
13607:
13600:
13556:
13551:
13546:
13541:
13536:
13531:
13526:
13521:
13519:
13479:
13459:
13450:
13430:
13425:
13420:
13415:
13410:
13405:
13400:
13398:
13392:
13387:
13382:
13377:
13372:
13370:
13369:
13364:
13359:
13354:
13349:
13344:
13339:
13334:
13332:
13321:
13316:Schläfli symbol
13295:
13290:
13285:
13274:
13256:
13233:
13194:
13160:
13149:
13148:
13147:
13145:
13142:
13141:
13135:
13130:
13125:
13120:
13115:
13110:
13105:
13103:
13100:Coxeter diagram
13088:
13078:
13074:
13070:
13068:
13037:
13032:
13027:
13022:
13017:
13015:
13008:
13003:
12998:
12993:
12988:
12983:
12978:
12976:
12972:Coxeter diagram
12931:
12924:
12898:
12887:
12886:
12885:
12883:
12880:
12879:
12874:
12858:
12847:
12846:
12845:
12843:
12840:
12839:
12810:Coxeter diagram
12806:
12721:
12704:
12679:, and its dual
12612:
12600:
12596:
12589:
12566:
12555:
12554:
12553:
12551:
12548:
12547:
12533:
12509:
12504:
12484:
12475:
12455:
12450:
12445:
12440:
12435:
12430:
12425:
12423:
12417:
12412:
12407:
12402:
12397:
12395:
12394:
12389:
12384:
12379:
12374:
12369:
12364:
12359:
12357:
12353:Coxeter diagram
12346:
12344:
12337:Schläfli symbol
12316:
12293:
12288:
12283:
12278:
12273:
12268:
12263:
12261:
12259:Coxeter diagram
12243:
12238:
12198:
12188:
12184:
12180:
12178:
12128:
12123:
12118:
12113:
12108:
12106:
12099:
12094:
12089:
12084:
12079:
12074:
12069:
12067:
12063:Coxeter diagram
12054:
12047:
12021:
12010:
12009:
12008:
12006:
12003:
12002:
11997:
11981:
11970:
11969:
11968:
11966:
11963:
11962:
11926:
11841:
11827:
11810:
11786:, and its dual
11719:
11693:
11682:
11681:
11680:
11678:
11675:
11674:
11662:
11658:
11651:
11640:
11619:
11610:
11590:
11585:
11580:
11575:
11570:
11565:
11560:
11558:
11552:
11547:
11542:
11537:
11532:
11530:
11529:
11524:
11519:
11514:
11509:
11504:
11499:
11494:
11492:
11488:Coxeter diagram
11481:
11479:
11472:Schläfli symbol
11451:
11446:
11437:
11415:
11410:
11405:
11400:
11395:
11393:
11386:
11381:
11376:
11374:
11367:
11362:
11357:
11352:
11347:
11345:
11338:
11333:
11328:
11323:
11318:
11313:
11308:
11306:
11299:
11294:
11289:
11287:
11283:Coxeter diagram
11230:
11223:
11216:
11209:
11182:
11177:
11172:
11167:
11162:
11160:
11154:
11149:
11144:
11139:
11134:
11132:
11126:
11121:
11116:
11111:
11106:
11101:
11096:
11094:
11057:
11031:
11020:
11019:
11018:
11016:
11013:
11012:
10970:
10950:
10945:
10940:
10935:
10930:
10925:
10920:
10918:
10912:
10907:
10902:
10897:
10892:
10890:
10889:
10884:
10879:
10874:
10869:
10864:
10859:
10854:
10852:
10846:
10841:
10836:
10831:
10826:
10824:
10823:
10818:
10813:
10808:
10803:
10798:
10793:
10788:
10786:
10780:
10775:
10770:
10765:
10760:
10758:
10757:
10752:
10747:
10742:
10737:
10732:
10727:
10722:
10720:
10709:
10707:
10702:Schläfli symbol
10681:
10676:
10656:
10630:
10615:
10570:
10568:
10561:
10557:
10553:
10549:
10545:
10541:
10539:
10480:
10453:
10432:
10417:
10408:
10393:
10388:
10383:
10381:
10374:
10369:
10364:
10359:
10354:
10352:
10345:
10340:
10335:
10330:
10325:
10323:
10316:
10311:
10306:
10301:
10296:
10291:
10286:
10284:
10277:
10272:
10267:
10265:
10261:Coxeter diagram
10251:
10246:
10241:
10239:
10238:
10236:
10234:
10217:
10206:
10205:
10204:
10202:
10199:
10198:
10191:
10186:
10181:
10176:
10171:
10169:
10168:
10166:
10165:
10149:
10138:
10137:
10136:
10134:
10131:
10130:
10123:
10118:
10113:
10108:
10103:
10101:
10095:
10090:
10085:
10080:
10075:
10073:
10072:
10070:
10069:
10053:
10042:
10041:
10040:
10038:
10035:
10034:
10027:
10022:
10017:
10015:
10009:
10004:
9999:
9994:
9989:
9984:
9979:
9977:
9976:
9974:
9973:
9957:
9946:
9945:
9944:
9942:
9939:
9938:
9931:
9926:
9921:
9919:
9913:
9908:
9903:
9898:
9893:
9888:
9883:
9881:
9880:
9878:
9876:
9859:
9848:
9847:
9846:
9844:
9841:
9840:
9805:
9798:
9791:
9784:
9777:
9735:
9724:
9723:
9722:
9720:
9717:
9716:
9701:
9576:
9526:edge-transitive
9522:cell-transitive
9465:edge-transitive
9446:
9442:
9417:
9406:
9405:
9404:
9402:
9399:
9398:
9387:
9385:
9380:
9372:
9368:
9357:
9325:
9294:
9289:
9284:
9279:
9274:
9269:
9264:
9262:
9251:
9247:
9242:Schläfli symbol
9206:
9201:
9196:
9185:
9167:
9133:
9128:
9123:
9118:
9113:
9108:
9103:
9101:
9094:
9089:
9084:
9079:
9074:
9069:
9064:
9062:
9056:
9051:
9046:
9041:
9036:
9034:
9030:Coxeter diagram
9002:
8995:
8983:
8967:
8956:
8955:
8954:
8952:
8949:
8948:
8929:
8918:
8917:
8916:
8914:
8911:
8910:
8877:
8792:
8770:, and its dual
8747:truncated cubes
8707:
8680:
8669:
8668:
8667:
8665:
8662:
8661:
8650:
8646:
8639:
8627:
8608:
8588:
8568:
8563:
8558:
8553:
8548:
8543:
8538:
8536:
8530:
8525:
8520:
8515:
8510:
8508:
8507:
8502:
8497:
8492:
8487:
8482:
8477:
8472:
8470:
8459:
8457:
8450:Schläfli symbol
8429:
8424:
8419:
8397:
8376:
8368:
8363:
8358:
8353:
8348:
8343:
8338:
8336:
8312:
8310:
8309:
8308:
8301:
8299:
8298:
8297:
8290:
8288:
8287:
8286:
8279:
8277:
8276:
8275:
8268:
8266:
8221:
8216:
8211:
8206:
8201:
8199:
8192:
8187:
8182:
8177:
8172:
8170:
8163:
8158:
8153:
8148:
8143:
8141:
8132:
8127:
8122:
8117:
8112:
8107:
8102:
8100:
8093:
8088:
8083:
8078:
8073:
8068:
8063:
8061:
8054:
8049:
8044:
8039:
8034:
8029:
8024:
8022:
8015:
8010:
8005:
8000:
7995:
7990:
7985:
7983:
7978:
7937:
7933:
7928:
7924:
7919:
7915:
7910:
7906:
7880:
7869:
7868:
7867:
7865:
7862:
7861:
7859:
7841:
7830:
7829:
7828:
7826:
7823:
7822:
7820:
7802:
7791:
7790:
7789:
7787:
7784:
7783:
7781:
7763:
7752:
7751:
7750:
7748:
7745:
7744:
7743:
7730:Coxeter diagram
7716:There are four
7714:
7629:
7605:cuboctahedrille
7559:edge-transitive
7540:
7513:
7502:
7501:
7500:
7498:
7495:
7494:
7483:
7479:
7472:
7461:
7442:
7422:
7402:
7397:
7392:
7387:
7382:
7377:
7372:
7370:
7364:
7359:
7354:
7349:
7344:
7342:
7336:
7331:
7326:
7321:
7316:
7314:
7308:
7303:
7298:
7293:
7288:
7286:
7285:
7280:
7275:
7270:
7265:
7260:
7255:
7250:
7248:
7242:
7237:
7232:
7227:
7222:
7220:
7219:
7214:
7209:
7204:
7199:
7194:
7189:
7184:
7182:
7176:
7171:
7166:
7161:
7156:
7154:
7153:
7148:
7143:
7138:
7133:
7128:
7123:
7118:
7116:
7105:
7103:
7101:
7099:
7092:Schläfli symbol
7071:
7066:
7061:
7051:
7046:
7041:
7039:
7020:
7009:
7008:
7007:
7005:
7002:
7001:
6999:
6982:
6971:
6970:
6969:
6967:
6964:
6963:
6959:
6951:
6947:
6941:
6931:
6926:
6921:
6919:
6900:
6889:
6888:
6887:
6885:
6882:
6881:
6879:
6862:
6851:
6850:
6849:
6847:
6844:
6843:
6835:
6830:
6825:
6823:
6821:
6816:
6811:
6806:
6804:
6800:
6784:
6781:
6775:
6765:
6760:
6755:
6750:
6745:
6743:
6725:
6714:
6713:
6712:
6710:
6707:
6706:
6704:
6703:
6684:
6673:
6672:
6671:
6669:
6666:
6665:
6658:
6653:
6648:
6643:
6638:
6633:
6628:
6626:
6624:
6619:
6614:
6609:
6604:
6599:
6597:
6593:
6577:
6573:
6567:
6557:
6552:
6547:
6545:
6542:
6523:
6512:
6511:
6510:
6508:
6505:
6504:
6497:
6492:
6487:
6482:
6477:
6472:
6467:
6465:
6463:
6458:
6453:
6448:
6446:
6442:
6426:
6422:
6416:
6406:
6401:
6396:
6391:
6386:
6384:
6382:
6372:
6367:
6362:
6357:
6352:
6350:
6332:
6321:
6320:
6319:
6317:
6314:
6313:
6311:
6310:
6291:
6280:
6279:
6278:
6276:
6273:
6272:
6265:
6260:
6255:
6250:
6245:
6243:
6241:
6236:
6231:
6226:
6221:
6216:
6214:
6210:
6194:
6190:
6166:
6155:
6154:
6153:
6151:
6148:
6147:
6140:
6135:
6130:
6125:
6120:
6118:
6101:
6097:
6087:
6082:
6076:
6069:
6057:
6021:
6010:
6009:
6008:
6006:
6003:
6002:
5989:
5981:
5976:
5971:
5966:
5961:
5959:
5956:
5948:
5943:
5938:
5933:
5928:
5926:
5923:
5915:
5910:
5905:
5900:
5895:
5893:
5890:
5882:
5877:
5872:
5867:
5862:
5860:
5857:
5849:
5844:
5839:
5834:
5829:
5827:
5824:
5816:
5811:
5806:
5801:
5796:
5794:
5791:
5783:
5778:
5773:
5768:
5763:
5761:
5750:
5745:
5740:
5735:
5730:
5728:
5718:
5714:
5707:
5699:
5694:
5689:
5684:
5679:
5677:
5674:
5666:
5661:
5656:
5651:
5646:
5644:
5634:
5629:
5624:
5619:
5614:
5612:
5610:
5605:
5600:
5595:
5590:
5585:
5583:
5579:
5571:
5567:
5560:
5552:
5547:
5542:
5537:
5532:
5530:
5527:
5519:
5514:
5509:
5504:
5499:
5497:
5494:
5486:
5481:
5476:
5471:
5466:
5464:
5461:
5453:
5448:
5443:
5438:
5433:
5431:
5421:
5416:
5411:
5406:
5401:
5396:
5391:
5389:
5387:
5382:
5377:
5372:
5367:
5362:
5360:
5356:
5349:
5345:
5332:
5326:
5314:
5292:
5287:
5282:
5277:
5272:
5270:
5261:
5253:
5248:
5243:
5241:
5238:
5230:
5225:
5220:
5218:
5215:
5207:
5202:
5197:
5195:
5184:
5179:
5174:
5172:
5162:
5158:
5150:
5142:
5137:
5132:
5130:
5120:
5115:
5110:
5108:
5106:
5101:
5096:
5091:
5089:
5085:
5077:
5073:
5065:
5057:
5052:
5047:
5045:
5035:
5030:
5025:
5023:
5013:
5009:
5002:
4994:
4989:
4984:
4979:
4974:
4969:
4964:
4962:
4959:
4951:
4946:
4941:
4936:
4931:
4926:
4921:
4919:
4916:
4908:
4903:
4898:
4893:
4888:
4883:
4878:
4876:
4873:
4865:
4860:
4855:
4850:
4845:
4840:
4835:
4833:
4823:
4818:
4813:
4808:
4803:
4801:
4799:
4794:
4789:
4784:
4779:
4774:
4769:
4764:
4762:
4758:
4751:
4747:
4740:
4732:
4727:
4722:
4717:
4712:
4707:
4702:
4700:
4697:
4689:
4684:
4679:
4674:
4669:
4664:
4659:
4657:
4656:
4653:
4645:
4640:
4635:
4630:
4625:
4620:
4615:
4613:
4610:
4602:
4597:
4592:
4587:
4582:
4577:
4572:
4570:
4567:
4559:
4554:
4549:
4544:
4539:
4534:
4529:
4527:
4524:
4516:
4511:
4506:
4501:
4496:
4491:
4486:
4484:
4474:
4469:
4464:
4459:
4454:
4449:
4444:
4442:
4433:
4429:
4416:
4410:
4398:
4372:
4367:
4362:
4357:
4352:
4347:
4342:
4340:
4337:
4329:
4314:
4304:
4289:
4277:
4266:
4255:
4244:
4233:
4222:
4211:
4202:
4193:
4182:
4171:
4160:
4149:
4138:
4127:
3968:
3963:
3958:
3953:
3951:
3950:
3945:
3940:
3935:
3930:
3925:
3923:
3922:
3918:
3906:
3901:
3896:
3891:
3889:
3888:
3883:
3878:
3873:
3868:
3863:
3861:
3860:
3856:
3844:
3839:
3834:
3829:
3824:
3822:
3821:
3817:
3805:
3800:
3795:
3793:
3792:
3787:
3782:
3777:
3772:
3767:
3765:
3764:
3760:
3748:
3743:
3738:
3733:
3728:
3726:
3725:
3721:
3709:
3704:
3699:
3697:
3696:
3691:
3686:
3681:
3676:
3671:
3669:
3668:
3664:
3652:
3647:
3642:
3637:
3632:
3630:
3629:
3625:
3613:
3608:
3603:
3598:
3593:
3591:
3590:
3587:
3522:
3517:
3512:
3507:
3502:
3497:
3495:
3494:
3489:
3484:
3479:
3474:
3469:
3464:
3459:
3457:
3456:
3445:
3440:
3435:
3430:
3425:
3420:
3418:
3417:
3412:
3407:
3402:
3397:
3392:
3387:
3382:
3380:
3379:
3369:
3364:
3359:
3354:
3349:
3344:
3339:
3337:
3336:
3326:
3321:
3316:
3311:
3306:
3301:
3296:
3294:
3293:
3288:
3283:
3278:
3273:
3268:
3266:
3265:
3260:
3255:
3250:
3245:
3240:
3235:
3230:
3228:
3227:
3217:
3212:
3207:
3202:
3197:
3192:
3187:
3185:
3184:
3174:
3169:
3164:
3159:
3154:
3149:
3144:
3139:
3137:
3136:
3131:
3126:
3121:
3116:
3111:
3109:
3108:
3103:
3098:
3093:
3088:
3083:
3078:
3073:
3071:
3070:
3060:
3055:
3050:
3045:
3040:
3035:
3030:
3028:
3027:
3017:
3012:
3007:
3002:
2997:
2992:
2987:
2985:
2984:
2911:
2906:
2901:
2896:
2891:
2889:
2888:
2884:
2872:
2867:
2862:
2857:
2852:
2850:
2849:
2845:
2833:
2828:
2823:
2818:
2813:
2811:
2810:
2806:
2794:
2789:
2784:
2779:
2774:
2772:
2771:
2767:
2755:
2750:
2745:
2740:
2735:
2733:
2732:
2728:
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2711:
2706:
2701:
2696:
2694:
2693:
2689:
2677:
2672:
2667:
2662:
2657:
2655:
2654:
2650:
2579:
2574:
2569:
2564:
2559:
2554:
2549:
2544:
2542:
2541:
2536:
2531:
2526:
2521:
2516:
2511:
2506:
2501:
2499:
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2493:
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2478:
2473:
2471:
2470:
2465:
2460:
2455:
2450:
2445:
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2421:
2416:
2411:
2406:
2401:
2396:
2391:
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2384:
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2378:
2373:
2368:
2363:
2358:
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2348:
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2307:
2302:
2297:
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2264:
2259:
2254:
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2241:
2236:
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2226:
2221:
2216:
2211:
2206:
2204:
2203:
2193:
2188:
2183:
2178:
2173:
2168:
2163:
2161:
2160:
2155:
2150:
2145:
2140:
2135:
2130:
2125:
2123:
2122:
2117:
2112:
2107:
2102:
2097:
2095:
2094:
2089:
2084:
2079:
2074:
2069:
2064:
2059:
2057:
2056:
2046:
2041:
2036:
2031:
2026:
2024:
2023:
2018:
2013:
2008:
2003:
1998:
1993:
1988:
1986:
1985:
1975:
1970:
1965:
1960:
1955:
1950:
1945:
1940:
1938:
1937:
1932:
1927:
1922:
1917:
1912:
1907:
1902:
1897:
1895:
1894:
1889:
1884:
1879:
1874:
1869:
1867:
1866:
1861:
1856:
1851:
1846:
1841:
1836:
1831:
1829:
1828:
1818:
1813:
1808:
1803:
1798:
1796:
1795:
1790:
1785:
1780:
1775:
1770:
1765:
1760:
1758:
1757:
1676:Schläfli symbol
1665:
1576:cubic honeycomb
1572:
1546:
1541:
1536:
1531:
1526:
1521:
1516:
1514:
1508:
1503:
1498:
1493:
1488:
1483:
1478:
1473:
1471:
1446:
1441:
1436:
1431:
1426:
1421:
1416:
1411:
1409:
1391:
1381:
1376:
1371:
1366:
1361:
1356:
1351:
1346:
1341:
1339:
1315:
1310:
1305:
1300:
1295:
1290:
1285:
1280:
1278:
1276:
1271:
1266:
1261:
1256:
1251:
1246:
1241:
1236:
1231:
1229:
1216:
1206:
1201:
1196:
1194:
1188:
1186:
1169:
1159:
1154:
1149:
1144:
1139:
1134:
1129:
1127:
1121:
1119:
1097:
1092:
1087:
1082:
1077:
1072:
1067:
1065:
1059:
1054:
1049:
1044:
1039:
1037:
1031:
1029:
1006:
1001:
996:
991:
986:
981:
976:
974:
968:
963:
958:
953:
948:
943:
938:
933:
931:
930:
925:
920:
915:
910:
905:
900:
895:
893:
887:
885:
876:
871:Schläfli symbol
866:Coxeter diagram
859:
844:
831:
826:
821:
816:
811:
806:
801:
799:
789:
784:
779:
774:
769:
764:
759:
754:
749:
747:
740:
735:
730:
725:
720:
715:
710:
705:
700:
695:
690:
688:
681:Coxeter diagram
675:
667:
663:
658:
654:
650:
634:
630:
625:
620:
615:
610:
605:
556:
554:
549:
547:
542:
540:
535:
533:
528:
526:
521:
519:
503:
452:
436:
405:
333:Schläfli symbol
297:cubic honeycomb
269:
240:
229:
228:
227:
225:
222:
221:
210:
206:
199:
188:
143:
138:
133:
128:
123:
118:
113:
111:
107:Coxeter diagram
97:Schläfli symbol
91:
87:
83:
82:
78:
28:
23:
22:
15:
12:
11:
5:
18612:
18602:
18601:
18596:
18591:
18586:
18570:
18569:
18565:
18558:
18551:
18547:
18540:
18538:
18535:
18528:
18526:
18523:
18516:
18514:
18511:
18508:
18504:
18494:
18490:
18489:
18487:
18483:
18481:
18479:
18475:
18473:
18471:
18467:
18465:
18463:
18461:
18458:
18455:
18451:
18450:
18448:
18444:
18442:
18440:
18436:
18434:
18432:
18428:
18426:
18424:
18422:
18419:
18414:
18410:
18409:
18405:
18398:
18391:
18387:
18383:
18381:
18379:
18374:
18372:
18369:
18364:
18362:
18359:
18356:
18352:
18347:
18343:
18342:
18338:
18331:
18327:
18322:
18320:
18317:
18312:
18310:
18307:
18302:
18300:
18297:
18294:
18290:
18285:
18281:
18280:
18276:
18272:
18267:
18265:
18262:
18257:
18255:
18252:
18247:
18245:
18242:
18239:
18235:
18230:
18226:
18225:
18223:
18218:
18216:
18213:
18208:
18206:
18203:
18198:
18196:
18193:
18190:
18186:
18181:
18177:
18176:
18171:
18166:
18164:
18161:
18156:
18154:
18151:
18146:
18144:
18141:
18138:
18134:
18129:
18125:
18124:
18122:
18117:
18115:
18112:
18107:
18105:
18102:
18097:
18095:
18092:
18089:
18085:
18080:
18076:
18075:
18070:
18065:
18063:
18060:
18055:
18053:
18050:
18045:
18043:
18040:
18037:
18033:
18031:Uniform tiling
18028:
18024:
18023:
18010:
18007:
18004:
17997:
17994:
17968:
17961:
17958:
17932:
17925:
17922:
17908:
17895:
17892:
17889:
17882:
17879:
17865:
17852:
17849:
17846:
17839:
17836:
17822:
17809:
17806:
17803:
17796:
17793:
17779:
17766:
17763:
17760:
17753:
17750:
17736:
17731:
17727:
17726:
17715:
17713:
17712:
17705:
17698:
17690:
17685:
17684:
17679:
17670:
17660:
17659:
17658:
17636:
17633:Geombinatorics
17626:
17616:
17597:
17578:John H. Conway
17572:
17571:
17560:
17551:
17536:
17526:
17525:
17523:
17520:
17519:
17518:
17513:
17508:
17502:
17497:
17492:
17485:
17482:
17393:
17392:
17391:, non-uniform
17386:
17382:
17381:
17379:
17373:
17372:
17365:
17361:
17360:
17349:
17345:
17344:
17325:
17321:
17320:
17223:
17217:
17216:
17212:
17206:
17203:
17197:
17196:
17191:
17187:
17186:
17179:
17176:
17120:
17119:
17114:
17110:
17109:
17097:
17093:
17092:
17089:
17083:
17082:
17071:
17067:
17066:
17047:
17043:
17042:
16945:
16939:
16938:
16933:
16927:
16926:
16921:
16917:
16916:
16909:
16906:
16850:
16849:
16844:
16840:
16839:
16827:
16823:
16822:
16820:
16814:
16813:
16802:
16798:
16797:
16778:
16774:
16773:
16676:
16670:
16669:
16665:
16659:
16656:
16650:
16649:
16644:
16640:
16639:
16632:
16629:
16622:
16607:
16551:
16550:
16549:, non-uniform
16544:
16540:
16539:
16531:
16527:
16526:
16523:
16517:
16516:
16503:
16497:
16496:
16485:
16481:
16480:
16461:
16457:
16453:
16452:
16413:
16407:
16406:
16402:
16399:
16393:
16392:
16387:
16383:
16382:
16375:
16372:
16365:
16354:
16335:
16275:
16274:
16273:, non-uniform
16268:
16264:
16263:
16255:
16251:
16250:
16248:
16242:
16241:
16234:
16230:
16229:
16218:
16214:
16213:
16176:
16172:
16168:
16167:
16128:
16122:
16121:
16117:
16114:
16108:
16107:
16102:
16098:
16097:
16090:
16087:
16083:
16082:
16075:
16068:
16061:
16053:
16052:
16045:
16038:
16031:
16013:
16012:
15984:
15983:
15978:
15974:
15973:
15968:
15964:
15963:
15960:
15954:
15953:
15940:
15939:Vertex figures
15936:
15935:
15928:
15924:
15923:
15884:
15878:
15877:
15873:
15870:
15864:
15863:
15860:
15856:
15855:
15848:
15845:
15765:
15764:
15763:, non-uniform
15758:
15754:
15753:
15748:
15744:
15743:
15740:
15734:
15733:
15721:
15717:
15716:
15705:
15701:
15700:
15672:
15668:
15667:
15628:
15622:
15621:
15617:
15614:
15608:
15607:
15602:
15598:
15597:
15590:
15587:
15524:
15502:
15499:
15496:
15495:
15488:
15480:
15479:
15470:
15446:
15443:
15440:
15439:
15432:
15425:
15419:
15418:
15399:
15360:
15354:
15353:
15346:
15339:
15335:
15334:
15331:
15328:
15322:
15321:
15314:
15307:
15301:
15300:
15286:
15279:
15276:
15262:
15248:
15241:
15238:
15224:
15197:
15194:
15191:
15190:
15183:
15176:
15169:
15165:
15164:
15157:
15150:
15143:
15139:
15138:
15135:
15132:
15129:
15112:
15109:
15108:
15107:
15043:
15042:
15037:
15033:
15032:
15020:
15016:
15015:
15002:
14995:
14992:
14977:
14971:
14970:
14957:
14947:Symmetry group
14943:
14942:
14931:
14925:
14924:
14908:
14904:
14903:
14884:
14880:
14879:
14840:
14834:
14833:
14829:
14826:
14820:
14819:
14814:
14810:
14809:
14802:
14799:
14762:
14740:
14737:
14736:
14735:
14710:
14703:
14700:
14635:
14632:
14631:
14630:
14605:
14602:
14599:
14598:
14591:
14584:
14577:
14573:
14572:
14565:
14558:
14551:
14547:
14546:
14543:
14540:
14537:
14520:
14517:
14514:
14513:
14506:
14499:
14492:
14368:
14367:
14362:
14358:
14357:
14345:
14341:
14340:
14331:
14321:
14320:
14307:
14300:
14297:
14282:
14276:
14275:
14261:
14255:
14254:
14238:
14234:
14233:
14196:
14192:
14191:
14152:
14146:
14145:
14141:
14138:
14132:
14131:
14126:
14122:
14121:
14114:
14111:
14078:
14060:
14057:
14051:
14040:
14029:
13961:
13960:
13959:, non-uniform
13954:
13950:
13949:
13941:
13937:
13936:
13934:
13928:
13927:
13920:
13914:
13913:
13902:
13898:
13897:
13869:
13865:
13861:
13860:
13821:
13815:
13814:
13810:
13807:
13801:
13800:
13795:
13791:
13790:
13783:
13780:
13776:
13775:
13730:
13598:
13575:
13574:
13573:, non-uniform
13568:
13564:
13563:
13517:
13513:
13512:
13510:
13504:
13503:
13491:
13485:
13484:
13473:
13469:
13468:
13440:
13436:
13435:
13330:
13324:
13323:
13318:
13312:
13311:
13306:
13302:
13301:
13294:
13291:
13254:
13232:
13229:
13226:
13225:
13218:
13193:
13190:
13189:
13188:
13163:
13156:
13153:
13087:
13084:
13081:
13080:
13076:
13072:
13064:
13063:
13056:
13049:
13043:
13042:
13013:
12974:
12968:
12967:
12960:
12953:
12949:
12948:
12945:
12942:
12936:
12935:
12928:
12921:
12915:
12914:
12901:
12894:
12891:
12876:
12861:
12854:
12851:
12836:
12830:
12829:
12826:
12823:
12805:
12802:
12799:
12798:
12791:
12784:
12777:
12773:
12772:
12765:
12758:
12751:
12747:
12746:
12743:
12740:
12737:
12720:
12717:
12716:
12715:
12703:
12700:
12699:
12698:
12630:
12629:
12624:
12620:
12619:
12607:
12603:
12602:
12593:
12587:Symmetry group
12583:
12582:
12569:
12562:
12559:
12544:
12538:
12537:
12521:
12515:
12514:
12498:
12494:
12493:
12465:
12461:
12460:
12355:
12349:
12348:
12342:
12341:tr{4,3,4} or t
12339:
12333:
12332:
12327:
12323:
12322:
12315:
12312:
12311:
12310:
12242:
12239:
12197:
12194:
12191:
12190:
12186:
12182:
12174:
12173:
12166:
12159:
12153:
12152:
12145:
12138:
12134:
12133:
12104:
12065:
12059:
12058:
12051:
12044:
12038:
12037:
12024:
12017:
12014:
11999:
11984:
11977:
11974:
11959:
11953:
11952:
11949:
11946:
11934:Coxeter groups
11925:
11922:
11919:
11918:
11911:
11904:
11897:
11893:
11892:
11885:
11878:
11871:
11867:
11866:
11863:
11860:
11857:
11840:
11837:
11834:
11833:
11820:
11809:
11806:
11805:
11804:
11737:
11736:
11731:
11727:
11726:
11714:
11710:
11709:
11696:
11689:
11686:
11671:
11665:
11664:
11655:
11645:
11644:
11633:
11629:
11628:
11600:
11596:
11595:
11490:
11484:
11483:
11477:
11476:rr{4,3,4} or t
11474:
11468:
11467:
11462:
11458:
11457:
11450:
11447:
11443:
11442:
11439:
11434:
11431:
11428:
11425:
11421:
11420:
11391:
11372:
11343:
11304:
11285:
11279:
11278:
11276:
11273:
11271:
11269:
11266:
11260:
11259:
11256:
11253:
11250:
11247:
11244:
11238:
11237:
11234:
11227:
11220:
11213:
11206:
11076:
11075:
11074:, non-uniform
11069:
11065:
11064:
11052:
11048:
11047:
11034:
11027:
11024:
11009:
11003:
11002:
10995:
10991:
10990:
10984:
10980:
10979:
10960:
10956:
10955:
10718:
10712:
10711:
10704:
10698:
10697:
10692:
10688:
10687:
10680:
10677:
10654:
10628:
10614:
10611:
10608:
10607:
10600:
10593:
10586:
10579:
10572:
10564:
10563:
10559:
10555:
10551:
10547:
10543:
10535:
10534:
10527:
10520:
10513:
10506:
10499:
10493:
10492:
10477:
10450:
10429:
10414:
10405:
10399:
10398:
10379:
10350:
10321:
10282:
10263:
10257:
10256:
10220:
10213:
10210:
10196:
10152:
10145:
10142:
10128:
10056:
10049:
10046:
10032:
9960:
9953:
9950:
9936:
9862:
9855:
9852:
9838:
9832:
9831:
9828:
9825:
9822:
9819:
9816:
9810:
9809:
9802:
9795:
9788:
9781:
9774:
9756:Coxeter groups
9738:
9731:
9728:
9700:
9697:
9694:
9693:
9686:
9679:
9672:
9665:
9658:
9654:
9653:
9646:
9639:
9632:
9625:
9618:
9614:
9613:
9610:
9607:
9604:
9575:
9572:
9469:
9468:
9458:
9454:
9453:
9439:
9435:
9434:
9420:
9413:
9410:
9396:
9390:
9389:
9376:
9366:Symmetry group
9362:
9361:
9350:
9344:
9343:
9337:
9331:
9330:
9319:
9315:
9314:
9304:
9300:
9299:
9260:
9254:
9253:
9249:
9244:
9238:
9237:
9232:
9228:
9227:
9213:
9212:
9205:
9202:
9166:
9163:
9160:
9159:
9152:
9145:
9139:
9138:
9099:
9032:
9026:
9025:
9018:
9011:
9007:
9006:
8999:
8992:
8986:
8985:
8970:
8963:
8960:
8945:
8932:
8925:
8922:
8907:
8901:
8900:
8897:
8894:
8885:Coxeter groups
8876:
8873:
8870:
8869:
8862:
8855:
8848:
8844:
8843:
8836:
8829:
8822:
8818:
8817:
8814:
8811:
8808:
8791:
8788:
8755:square pyramid
8725:
8724:
8719:
8715:
8714:
8702:
8698:
8697:
8683:
8676:
8673:
8659:
8653:
8652:
8643:
8633:
8632:
8630:square pyramid
8620:
8614:
8613:
8602:
8598:
8597:
8578:
8574:
8573:
8468:
8462:
8461:
8455:
8452:
8446:
8445:
8440:
8436:
8435:
8428:
8425:
8396:
8393:
8392:
8391:
8377:{2,6,3}, with
8374:
8373:, and symbol s
8315:
8314:
8306:
8303:
8295:
8292:
8284:
8281:
8273:
8270:
8262:
8261:
8254:
8247:
8240:
8233:
8227:
8226:
8197:
8168:
8138:
8137:
8098:
8059:
8020:
7981:
7973:
7972:
7965:
7958:
7951:
7944:
7940:
7939:
7930:
7921:
7912:
7903:
7897:
7896:
7883:
7876:
7873:
7857:
7844:
7837:
7834:
7818:
7805:
7798:
7795:
7779:
7766:
7759:
7756:
7741:
7728:name, and the
7713:
7710:
7707:
7706:
7699:
7692:
7685:
7681:
7680:
7673:
7666:
7659:
7655:
7654:
7651:
7648:
7645:
7628:
7625:
7562:
7561:
7552:
7548:
7547:
7535:
7531:
7530:
7516:
7509:
7506:
7492:
7486:
7485:
7476:
7466:
7465:
7454:
7448:
7447:
7436:
7432:
7431:
7412:
7408:
7407:
7114:
7108:
7107:
7097:
7094:
7088:
7087:
7082:
7078:
7077:
7070:
7067:
7063:
7062:
7057:
7037:
7023:
7016:
7013:
6985:
6978:
6975:
6961:
6956:
6953:
6943:
6942:
6937:
6917:
6903:
6896:
6893:
6865:
6858:
6855:
6840:
6802:
6797:
6789:
6786:
6777:
6776:
6771:
6741:
6728:
6721:
6718:
6701:
6687:
6680:
6677:
6663:
6595:
6590:
6582:
6579:
6569:
6568:
6563:
6543:
6540:
6526:
6519:
6516:
6502:
6444:
6439:
6431:
6428:
6418:
6417:
6412:
6378:
6348:
6335:
6328:
6325:
6308:
6294:
6287:
6284:
6270:
6212:
6207:
6199:
6196:
6186:
6185:
6182:
6169:
6162:
6159:
6145:
6116:
6114:
6106:
6103:
6093:
6092:
6089:
6084:
6079:
6072:
6065:
6060:
6052:
6051:
6050:A3 honeycombs
6024:
6017:
6014:
5993:
5992:
5987:
5954:
5921:
5888:
5855:
5822:
5789:
5758:
5755:
5726:
5723:
5720:
5710:
5709:
5705:
5672:
5642:
5639:
5581:
5576:
5573:
5563:
5562:
5558:
5525:
5492:
5459:
5429:
5426:
5358:
5354:
5351:
5341:
5340:
5337:
5334:
5329:
5322:
5317:
5309:
5308:
5307:B3 honeycombs
5265:
5264:
5259:
5236:
5213:
5192:
5189:
5170:
5167:
5164:
5154:
5153:
5148:
5128:
5125:
5087:
5082:
5079:
5069:
5068:
5063:
5043:
5040:
5021:
5018:
5015:
5005:
5004:
5000:
4957:
4914:
4871:
4831:
4828:
4760:
4756:
4753:
4743:
4742:
4738:
4695:
4651:
4608:
4565:
4522:
4482:
4479:
4440:
4438:
4435:
4425:
4424:
4421:
4418:
4413:
4406:
4401:
4393:
4392:
4391:C3 honeycombs
4336:
4333:
4327:
4302:
4288:
4285:
4282:
4281:
4270:
4259:
4248:
4237:
4226:
4215:
4204:
4198:
4197:
4186:
4175:
4164:
4153:
4142:
4131:
4120:
4116:
4115:
4108:
4101:
4094:
4087:
4080:
4073:
4066:
4062:
4061:
4055:
4050:
4045:
4040:
4035:
4030:
4025:
4021:
4020:
4017:
4014:
4011:
4008:
4005:
4001:
4000:
3995:
3992:
3987:
3983:
3982:
3974:
3973:
3911:
3849:
3810:
3753:
3714:
3657:
3618:
3582:
3581:
3574:
3567:
3560:
3553:
3546:
3539:
3532:
3528:
3527:
3450:
3374:
3331:
3222:
3179:
3065:
3022:
2980:
2979:
2976:
2973:
2970:
2967:
2964:
2960:
2959:
2954:
2949:
2944:
2940:
2939:
2917:
2916:
2877:
2838:
2799:
2760:
2721:
2682:
2643:
2639:
2638:
2631:
2624:
2617:
2610:
2603:
2596:
2589:
2585:
2584:
2426:
2269:
2198:
2051:
1980:
1823:
1752:
1748:
1747:
1744:
1741:
1738:
1735:
1732:
1728:
1727:
1722:
1717:
1712:
1708:
1707:
1698:vertex figures
1664:
1661:
1658:
1657:
1650:
1643:
1636:
1632:
1631:
1624:
1617:
1610:
1606:
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1599:
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1554:
1551:
1469:
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1461:
1454:
1451:
1407:
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1403:
1400:
1393:
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1337:
1334:
1333:
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1320:
1227:
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1182:
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1178:
1171:
1167:
1164:
1125:
1116:
1115:
1112:
1105:
1102:
1035:
1025:
1024:
1021:
1014:
1011:
891:
882:
881:
878:
873:
868:
863:
843:
840:
837:
836:
797:
794:
745:
686:
683:
677:
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673:
671:
668:
665:
661:
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656:
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648:
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637:
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584:
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563:
559:
558:
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513:
512:
507:
500:
494:
488:
486:Parallelepiped
483:
477:
476:
471:
466:
461:
456:
447:
445:Crystal system
435:
432:
404:
401:
391:. Any finite
291:
290:
281:
277:
276:
264:
258:
257:
243:
236:
233:
219:
213:
212:
203:
193:
192:
181:
175:
174:
168:
164:
163:
153:
149:
148:
109:
103:
102:
99:
93:
92:
89:
85:
80:
76:
73:
69:
68:
63:
59:
58:
53:
49:
48:
35:
34:
26:
9:
6:
4:
3:
2:
18611:
18600:
18597:
18595:
18592:
18590:
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18561:
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18505:
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18499:
18495:
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18491:
18488:
18480:
18472:
18464:
18459:
18456:
18453:
18452:
18449:
18441:
18433:
18425:
18420:
18418:
18415:
18412:
18411:
18408:
18401:
18394:
18388:
18380:
18378:
18370:
18368:
18360:
18358:
18353:
18351:
18348:
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18344:
18341:
18334:
18328:
18326:
18318:
18316:
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18286:
18283:
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18279:
18273:
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18263:
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18214:
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18142:
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18135:
18133:
18130:
18127:
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18123:
18121:
18113:
18111:
18103:
18101:
18093:
18091:
18086:
18084:
18081:
18078:
18077:
18074:
18071:
18069:
18061:
18059:
18051:
18049:
18041:
18039:
18034:
18032:
18029:
18026:
18025:
18008:
18005:
18002:
17992:
17966:
17956:
17930:
17920:
17909:
17893:
17890:
17887:
17877:
17866:
17850:
17847:
17844:
17834:
17823:
17807:
17804:
17801:
17791:
17780:
17764:
17761:
17758:
17748:
17737:
17735:
17732:
17729:
17728:
17723:
17719:
17711:
17706:
17704:
17699:
17697:
17692:
17691:
17688:
17683:
17680:
17676:
17671:
17668:
17664:
17661:
17656:
17652:
17651:
17650:
17648:
17644:
17640:
17637:
17634:
17630:
17627:
17625:
17621:
17617:
17614:
17613:0-486-61480-8
17610:
17606:
17605:
17601:
17598:
17595:
17591:
17587:
17583:
17579:
17576:
17575:
17569:
17564:
17555:
17548:
17544:
17540:
17531:
17527:
17517:
17514:
17512:
17509:
17506:
17503:
17501:
17498:
17496:
17493:
17491:
17488:
17487:
17481:
17478:
17476:
17472:
17468:
17464:
17460:
17408:
17404:
17400:
17390:
17387:
17383:
17380:
17378:
17374:
17370:
17366:
17364:Vertex figure
17362:
17358:
17353:
17350:
17346:
17342:
17338:
17333:
17329:
17326:
17322:
17224:
17222:
17218:
17204:
17202:
17198:
17195:
17192:
17188:
17183:
17174:
17172:
17167:
17165:
17160:
17158:
17153:
17151:
17147:
17143:
17139:
17135:
17131:
17127:
17118:
17115:
17111:
17107:
17101:
17098:
17094:
17090:
17088:
17087:Coxeter group
17084:
17080:
17075:
17072:
17068:
17064:
17060:
17055:
17051:
17048:
17044:
16946:
16944:
16940:
16934:
16932:
16928:
16925:
16922:
16918:
16913:
16904:
16902:
16897:
16895:
16890:
16888:
16883:
16881:
16877:
16873:
16869:
16865:
16861:
16857:
16848:
16845:
16841:
16837:
16831:
16828:
16824:
16821:
16819:
16818:Coxeter group
16815:
16811:
16806:
16803:
16799:
16795:
16791:
16786:
16782:
16779:
16775:
16677:
16675:
16671:
16657:
16655:
16651:
16648:
16645:
16641:
16636:
16627:
16625:
16618:
16614:
16610:
16603:
16562:
16558:
16548:
16545:
16541:
16537:
16532:
16528:
16524:
16522:
16521:Coxeter group
16518:
16514:
16508:
16504:
16502:
16501:Vertex figure
16498:
16494:
16489:
16486:
16482:
16478:
16474:
16469:
16465:
16458:
16454:
16414:
16412:
16408:
16400:
16398:
16394:
16391:
16388:
16384:
16379:
16370:
16368:
16361:
16357:
16350:
16346:
16342:
16338:
16331:
16290:
16286:
16282:
16272:
16269:
16265:
16261:
16256:
16252:
16249:
16247:
16246:Coxeter group
16243:
16239:
16235:
16233:Vertex figure
16231:
16227:
16222:
16219:
16215:
16211:
16207:
16202:
16198:
16193:
16189:
16184:
16180:
16173:
16169:
16129:
16127:
16123:
16115:
16113:
16109:
16106:
16103:
16099:
16094:
16080:
16076:
16073:
16069:
16066:
16062:
16059:
16055:
16054:
16050:
16046:
16043:
16039:
16036:
16032:
16027:
16023:
16016:
16010:
16006:
16005:
16004:
16002:
15997:
15995:
15991:
15982:
15979:
15975:
15972:
15969:
15965:
15961:
15959:
15955:
15952:
15948:
15944:
15941:
15937:
15933:
15929:
15925:
15885:
15883:
15879:
15871:
15869:
15865:
15861:
15857:
15852:
15844:
15842:
15838:
15834:
15830:
15826:
15784:
15780:
15776:
15772:
15762:
15759:
15755:
15752:
15749:
15745:
15741:
15739:
15735:
15731:
15726:
15722:
15720:Vertex figure
15718:
15714:
15709:
15706:
15702:
15698:
15694:
15689:
15685:
15680:
15676:
15673:
15669:
15629:
15627:
15623:
15615:
15613:
15609:
15606:
15603:
15599:
15594:
15585:
15584:
15583:Vertex figure
15579:
15574:
15572:
15568:
15564:
15560:
15555:
15554:
15549:
15544:
15543:
15542:Vertex figure
15538:
15533:
15531:
15527:
15520:
15516:
15512:
15508:
15493:
15489:
15486:
15482:
15481:
15477:
15471:
15468:
15462:
15461:
15458:
15456:
15452:
15437:
15433:
15430:
15426:
15424:
15423:Vertex figure
15421:
15400:
15361:
15359:
15356:
15355:
15351:
15347:
15344:
15340:
15337:
15332:
15329:
15327:
15324:
15323:
15315:
15308:
15306:
15303:
15302:
15284:
15274:
15263:
15246:
15236:
15225:
15223:
15220:
15219:
15213:
15211:
15207:
15203:
15188:
15184:
15181:
15177:
15174:
15170:
15167:
15166:
15162:
15158:
15155:
15151:
15148:
15144:
15141:
15140:
15133:
15130:
15127:
15126:
15120:
15118:
15105:
15099:
15095:
15094:
15093:
15091:
15087:
15083:
15079:
15077:
15076:vertex figure
15074:
15070:
15066:
15062:
15058:
15054:
15050:
15041:
15038:
15034:
15030:
15024:
15021:
15017:
15000:
14990:
14978:
14976:
14975:Coxeter group
14972:
14965:
14958:
14956:
14952:
14948:
14944:
14941:
14936:
14932:
14930:
14929:Vertex figure
14926:
14922:
14917:
14912:
14909:
14905:
14901:
14897:
14892:
14888:
14885:
14881:
14841:
14839:
14835:
14827:
14825:
14821:
14818:
14815:
14811:
14806:
14797:
14796:
14791:
14786:
14785:
14784:Vertex figure
14780:
14775:
14773:
14769:
14765:
14758:
14754:
14750:
14746:
14733:
14729:
14728:
14727:
14724:
14708:
14698:
14649:
14645:
14641:
14628:
14623:
14619:
14618:
14617:
14615:
14611:
14596:
14592:
14589:
14585:
14582:
14578:
14575:
14574:
14570:
14566:
14563:
14559:
14556:
14552:
14549:
14548:
14541:
14538:
14535:
14534:
14528:
14526:
14511:
14507:
14504:
14500:
14497:
14493:
14490:
14486:
14485:
14482:
14480:
14476:
14472:
14468:
14466:
14462:
14420:
14415:
14413:
14412:vertex figure
14410:
14407:
14403:
14399:
14395:
14391:
14387:
14383:
14380:is a uniform
14379:
14375:
14366:
14363:
14359:
14355:
14349:
14346:
14342:
14332:
14330:
14326:
14322:
14305:
14295:
14283:
14281:
14280:Coxeter group
14277:
14274:
14271:
14266:
14262:
14260:
14259:Vertex figure
14256:
14252:
14247:
14242:
14239:
14235:
14231:
14227:
14222:
14218:
14213:
14209:
14204:
14200:
14197:
14193:
14153:
14151:
14147:
14139:
14137:
14133:
14130:
14127:
14123:
14118:
14109:
14108:
14103:
14098:
14097:
14096:Vertex figure
14092:
14087:
14085:
14081:
14074:
14070:
14066:
14056:
14054:
14047:
14043:
14036:
14032:
14025:
13984:
13980:
13976:
13972:
13968:
13958:
13955:
13951:
13947:
13942:
13938:
13935:
13933:
13932:Coxeter group
13929:
13925:
13921:
13919:
13918:Vertex figure
13915:
13911:
13906:
13903:
13899:
13895:
13891:
13886:
13882:
13877:
13873:
13866:
13862:
13822:
13820:
13816:
13808:
13806:
13802:
13799:
13796:
13792:
13787:
13735:
13731:
13690:
13686:
13682:
13678:
13611:
13605:
13601:
13594:
13590:
13586:
13582:
13572:
13569:
13565:
13561:
13518:
13514:
13511:
13509:
13508:Coxeter group
13505:
13501:
13496:
13492:
13490:
13489:Vertex figure
13486:
13482:
13477:
13474:
13470:
13466:
13462:
13457:
13453:
13448:
13444:
13441:
13437:
13331:
13329:
13325:
13319:
13317:
13313:
13310:
13307:
13303:
13298:
13289:
13288:
13283:
13278:
13277:
13276:Vertex figure
13272:
13267:
13265:
13261:
13257:
13250:
13246:
13242:
13238:
13223:
13219:
13216:
13212:
13211:
13205:
13203:
13199:
13186:
13182:
13181:
13180:
13177:
13161:
13151:
13101:
13097:
13093:
13077:
13073:
13066:
13061:
13057:
13054:
13050:
13048:
13047:Vertex figure
13045:
13044:
13014:
12975:
12973:
12970:
12969:
12965:
12961:
12958:
12954:
12951:
12946:
12943:
12941:
12938:
12937:
12929:
12922:
12920:
12917:
12916:
12899:
12889:
12877:
12859:
12849:
12837:
12835:
12834:Coxeter group
12832:
12827:
12824:
12822:Construction
12821:
12820:
12817:
12815:
12811:
12796:
12792:
12789:
12785:
12782:
12778:
12775:
12774:
12770:
12766:
12763:
12759:
12756:
12752:
12749:
12748:
12741:
12738:
12735:
12734:
12728:
12726:
12713:
12709:
12708:
12707:
12696:
12690:
12686:
12685:
12684:
12682:
12678:
12674:
12670:
12668:
12667:vertex figure
12665:
12661:
12657:
12653:
12649:
12645:
12641:
12637:
12628:
12625:
12621:
12617:
12611:
12608:
12604:
12594:
12592:
12588:
12584:
12567:
12557:
12545:
12543:
12542:Coxeter group
12539:
12536:
12531:
12526:
12522:
12520:
12519:Vertex figure
12516:
12512:
12507:
12502:
12499:
12495:
12491:
12487:
12482:
12478:
12473:
12469:
12466:
12462:
12356:
12354:
12350:
12340:
12338:
12334:
12331:
12328:
12324:
12319:
12308:
12304:
12303:
12302:
12299:
12260:
12256:
12252:
12248:
12237:
12235:
12231:
12227:
12223:
12219:
12215:
12211:
12210:cuboctahedron
12207:
12203:
12187:
12183:
12176:
12171:
12167:
12164:
12160:
12158:
12157:Vertex figure
12155:
12154:
12150:
12146:
12143:
12139:
12136:
12105:
12066:
12064:
12061:
12060:
12052:
12045:
12043:
12040:
12039:
12022:
12012:
12000:
11982:
11972:
11960:
11958:
11957:Coxeter group
11955:
11950:
11947:
11945:Construction
11944:
11943:
11937:
11935:
11931:
11916:
11912:
11909:
11905:
11902:
11898:
11895:
11894:
11890:
11886:
11883:
11879:
11876:
11872:
11869:
11868:
11861:
11858:
11855:
11854:
11848:
11846:
11831:
11825:
11821:
11818:
11814:
11802:
11797:
11793:
11792:
11791:
11789:
11785:
11781:
11777:
11775:
11774:vertex figure
11772:
11768:
11764:
11760:
11756:
11752:
11748:
11744:
11735:
11732:
11728:
11724:
11718:
11715:
11711:
11694:
11684:
11672:
11670:
11669:Coxeter group
11666:
11656:
11654:
11650:
11646:
11643:
11638:
11634:
11632:Vertex figure
11630:
11626:
11622:
11617:
11613:
11608:
11604:
11601:
11597:
11491:
11489:
11485:
11475:
11473:
11469:
11466:
11463:
11459:
11454:
11440:
11435:
11432:
11429:
11426:
11423:
11392:
11373:
11344:
11305:
11286:
11284:
11281:
11277:
11274:
11272:
11270:
11267:
11265:
11264:Coxeter group
11262:
11261:
11257:
11254:
11251:
11248:
11245:
11243:
11240:
11239:
11235:
11228:
11221:
11214:
11207:
11205:
11202:
11201:
11195:
11193:
11188:
11092:
11087:
11083:
11073:
11070:
11066:
11062:
11056:
11053:
11049:
11032:
11022:
11010:
11008:
11007:Coxeter group
11004:
11000:
10996:
10994:Vertex figure
10992:
10988:
10985:
10981:
10977:
10973:
10968:
10964:
10961:
10957:
10719:
10717:
10713:
10705:
10703:
10699:
10696:
10693:
10689:
10684:
10675:
10673:
10669:
10665:
10661:
10657:
10650:
10646:
10642:
10637:
10635:
10631:
10624:
10620:
10605:
10601:
10598:
10594:
10591:
10587:
10584:
10580:
10577:
10573:
10566:
10565:
10560:
10556:
10552:
10548:
10544:
10537:
10532:
10528:
10525:
10521:
10518:
10514:
10511:
10507:
10504:
10500:
10498:
10497:Vertex figure
10495:
10490:
10484:
10478:
10475:
10469:
10463:
10457:
10451:
10448:
10442:
10436:
10430:
10427:
10421:
10415:
10412:
10406:
10404:
10401:
10380:
10351:
10322:
10283:
10264:
10262:
10259:
10258:
10218:
10208:
10197:
10150:
10140:
10129:
10054:
10044:
10033:
9958:
9948:
9937:
9860:
9850:
9839:
9837:
9836:Coxeter group
9829:
9826:
9823:
9820:
9817:
9815:
9812:
9811:
9803:
9796:
9789:
9782:
9775:
9773:
9770:
9769:
9763:
9761:
9757:
9753:
9752:Coxeter group
9736:
9726:
9714:
9710:
9706:
9691:
9687:
9684:
9680:
9677:
9673:
9670:
9666:
9663:
9659:
9656:
9655:
9651:
9647:
9644:
9640:
9637:
9633:
9630:
9626:
9623:
9619:
9616:
9615:
9608:
9605:
9602:
9601:
9595:
9593:
9589:
9585:
9581:
9571:
9569:
9565:
9561:
9557:
9553:
9549:
9545:
9541:
9537:
9535:
9531:
9527:
9524:. It is also
9523:
9519:
9515:
9514:vertex figure
9512:
9508:
9504:
9500:
9496:
9492:
9488:
9484:
9475:
9466:
9462:
9459:
9455:
9451:
9445:
9440:
9436:
9418:
9408:
9397:
9395:
9394:Coxeter group
9391:
9384:
9377:
9375:
9371:
9367:
9363:
9360:
9355:
9351:
9349:
9348:Vertex figure
9345:
9341:
9338:
9336:
9332:
9328:
9323:
9320:
9316:
9312:
9308:
9305:
9301:
9261:
9259:
9255:
9245:
9243:
9239:
9236:
9233:
9229:
9225:
9219:
9214:
9209:
9200:
9199:
9194:
9189:
9188:
9187:Vertex figure
9183:
9178:
9176:
9172:
9157:
9153:
9150:
9146:
9144:
9143:Vertex figure
9141:
9100:
9033:
9031:
9028:
9023:
9019:
9016:
9012:
9009:
9000:
8993:
8991:
8988:
8987:
8968:
8958:
8946:
8930:
8920:
8908:
8906:
8905:Coxeter group
8903:
8898:
8895:
8893:Construction
8892:
8891:
8888:
8886:
8882:
8867:
8863:
8860:
8856:
8853:
8849:
8846:
8845:
8841:
8837:
8834:
8830:
8827:
8823:
8820:
8819:
8812:
8809:
8806:
8805:
8799:
8797:
8787:
8785:
8780:
8775:
8773:
8769:
8765:
8761:
8759:
8758:vertex figure
8756:
8752:
8748:
8744:
8740:
8736:
8732:
8723:
8720:
8716:
8712:
8706:
8703:
8699:
8681:
8671:
8660:
8658:
8657:Coxeter group
8654:
8644:
8642:
8638:
8634:
8631:
8625:
8621:
8619:
8618:Vertex figure
8615:
8611:
8606:
8603:
8599:
8595:
8591:
8586:
8582:
8579:
8575:
8469:
8467:
8463:
8454:t{4,3,4} or t
8453:
8451:
8447:
8444:
8441:
8437:
8432:
8423:
8422:
8417:
8412:
8410:
8406:
8402:
8388:
8384:
8383:
8382:
8380:
8334:
8330:
8326:
8322:
8304:
8293:
8282:
8271:
8264:
8259:
8255:
8252:
8248:
8245:
8241:
8238:
8234:
8232:
8231:Vertex figure
8229:
8198:
8169:
8140:
8099:
8060:
8021:
7980:
7970:
7966:
7963:
7959:
7956:
7952:
7949:
7945:
7942:
7931:
7922:
7913:
7904:
7902:
7899:
7898:
7881:
7871:
7858:
7842:
7832:
7819:
7803:
7793:
7780:
7764:
7754:
7742:
7740:
7737:
7733:
7731:
7727:
7723:
7722:Coxeter group
7719:
7704:
7700:
7697:
7693:
7690:
7686:
7683:
7682:
7678:
7674:
7671:
7667:
7664:
7660:
7657:
7656:
7649:
7646:
7643:
7642:
7636:
7634:
7624:
7622:
7617:
7612:
7610:
7606:
7602:
7598:
7596:
7595:vertex figure
7593:
7589:
7585:
7581:
7577:
7573:
7569:
7560:
7556:
7553:
7549:
7545:
7539:
7536:
7532:
7514:
7504:
7493:
7491:
7490:Coxeter group
7487:
7477:
7475:
7471:
7467:
7464:
7459:
7455:
7453:
7452:Vertex figure
7449:
7445:
7440:
7437:
7433:
7429:
7425:
7420:
7416:
7413:
7409:
7115:
7113:
7109:
7096:r{4,3,4} or t
7095:
7093:
7089:
7086:
7083:
7079:
7074:
7060:
7038:
7021:
7011:
6983:
6973:
6962:
6957:
6954:
6945:
6944:
6940:
6918:
6901:
6891:
6863:
6853:
6841:
6798:
6795:
6787:
6779:
6778:
6774:
6742:
6726:
6716:
6685:
6675:
6664:
6596:
6591:
6588:
6583:
6580:
6571:
6570:
6566:
6544:
6524:
6514:
6503:
6445:
6440:
6437:
6432:
6429:
6420:
6419:
6415:
6381:
6349:
6333:
6323:
6292:
6282:
6271:
6213:
6208:
6205:
6200:
6197:
6188:
6187:
6183:
6167:
6157:
6146:
6117:
6115:
6112:
6107:
6104:
6095:
6094:
6090:
6085:
6080:
6078:
6073:
6071:
6066:
6064:
6061:
6059:
6054:
6053:
6048:
6045:
6043:
6039:
6038:Coxeter group
6022:
6012:
6000:
5991:
5990:
5957:
5924:
5891:
5858:
5825:
5792:
5759:
5756:
5727:
5724:
5721:
5712:
5711:
5708:
5675:
5643:
5640:
5582:
5577:
5574:
5565:
5564:
5561:
5528:
5495:
5462:
5430:
5427:
5359:
5355:
5352:
5343:
5342:
5338:
5335:
5330:
5328:
5323:
5321:
5318:
5316:
5311:
5310:
5305:
5302:
5300:
5299:Coxeter group
5263:
5262:
5239:
5216:
5193:
5190:
5171:
5168:
5165:
5156:
5155:
5151:
5129:
5126:
5088:
5083:
5080:
5071:
5070:
5066:
5044:
5041:
5022:
5019:
5016:
5007:
5006:
5003:
4960:
4917:
4874:
4832:
4829:
4761:
4757:
4754:
4745:
4744:
4741:
4698:
4654:
4611:
4568:
4525:
4483:
4480:
4441:
4439:
4436:
4427:
4426:
4422:
4419:
4414:
4412:
4407:
4405:
4402:
4400:
4395:
4394:
4389:
4386:
4384:
4380:
4379:Coxeter group
4332:
4330:
4323:
4318:
4317:
4312:
4307:
4305:
4298:
4294:
4280:
4275:
4271:
4269:
4264:
4260:
4258:
4253:
4249:
4247:
4242:
4238:
4236:
4231:
4227:
4225:
4220:
4216:
4214:
4209:
4205:
4200:
4199:
4196:
4191:
4187:
4185:
4180:
4176:
4174:
4169:
4165:
4163:
4158:
4154:
4152:
4147:
4143:
4141:
4136:
4132:
4130:
4125:
4121:
4118:
4117:
4113:
4109:
4106:
4102:
4099:
4095:
4092:
4088:
4085:
4081:
4078:
4074:
4071:
4067:
4064:
4063:
4060:
4056:
4054:
4051:
4049:
4046:
4044:
4041:
4039:
4036:
4034:
4031:
4029:
4026:
4023:
4022:
4015:
4012:
4009:
4006:
4003:
4002:
3999:
3993:
3991:
3988:
3985:
3984:
3979:
3921:
3916:
3912:
3859:
3854:
3850:
3820:
3815:
3811:
3763:
3758:
3754:
3724:
3719:
3715:
3667:
3662:
3658:
3628:
3623:
3619:
3589:
3584:
3583:
3579:
3575:
3572:
3568:
3565:
3561:
3558:
3554:
3551:
3547:
3544:
3540:
3537:
3533:
3530:
3529:
3455:
3454:{4,3,∞}
3451:
3378:
3375:
3335:
3332:
3226:
3223:
3183:
3180:
3069:
3066:
3026:
3023:
2982:
2981:
2974:
2971:
2968:
2965:
2962:
2961:
2958:
2953:
2950:
2948:
2945:
2942:
2941:
2936:
2933:
2931:
2928:
2924:
2887:
2882:
2878:
2848:
2843:
2839:
2809:
2804:
2800:
2770:
2765:
2761:
2731:
2726:
2722:
2692:
2687:
2683:
2653:
2648:
2644:
2641:
2640:
2636:
2632:
2629:
2625:
2622:
2618:
2615:
2611:
2608:
2604:
2601:
2597:
2594:
2590:
2587:
2586:
2431:
2430:{∞,3,4}
2427:
2273:
2270:
2202:
2199:
2055:
2052:
1984:
1981:
1827:
1824:
1756:
1753:
1750:
1749:
1742:
1739:
1736:
1733:
1730:
1729:
1726:
1721:
1718:
1716:
1713:
1710:
1709:
1704:
1701:
1699:
1696:
1691:
1689:
1685:
1681:
1677:
1673:
1670:
1655:
1651:
1648:
1644:
1641:
1637:
1634:
1633:
1629:
1625:
1622:
1618:
1615:
1611:
1608:
1607:
1600:
1597:
1594:
1593:
1587:
1585:
1584:square tiling
1581:
1577:
1563:8: abcd/efgh
1562:
1559:
1555:
1552:
1470:
1467:
1463:4: abcd/abcd
1462:
1459:
1455:
1452:
1408:
1406:
1402:2: abba/abba
1401:
1398:
1394:
1387:
1338:
1336:
1332:2: aaaa/bbbb
1331:
1328:
1324:
1321:
1228:
1226:
1222:4: abbb/bbba
1221:
1219:
1212:
1193:
1184:
1180:4: abbc/bccd
1179:
1176:
1172:
1165:
1126:
1118:
1114:2: abba/baab
1113:
1110:
1106:
1103:
1036:
1027:
1023:1: aaaa/aaaa
1022:
1019:
1015:
1012:
892:
884:
879:
874:
872:
869:
867:
864:
862:
858:
855:
854:
851:
849:
798:
795:
746:
687:
684:
682:
679:
672:
669:
660:
647:
644:
642:
639:
628:
623:
618:
613:
608:
604:
601:
596:
592:
589:
585:
582:
578:
575:
571:
568:
564:
561:
552:
545:
538:
531:
524:
518:
515:
511:
508:
506:
505:trapezohedron
501:
499:
495:
493:
489:
487:
484:
482:
479:
475:
472:
470:
467:
465:
462:
460:
457:
455:
451:
448:
446:
443:
442:
439:
431:
429:
425:
420:
418:
417:square tiling
414:
410:
400:
398:
394:
390:
386:
382:
378:
373:
371:
370:
365:
361:
357:
353:
352:space-filling
349:
344:
342:
338:
334:
330:
326:
323:is a regular
322:
321:vertex figure
318:
314:
310:
306:
302:
298:
289:
285:
282:
278:
274:
268:
265:
263:
259:
241:
231:
220:
218:
217:Coxeter group
214:
204:
202:
198:
194:
191:
186:
182:
180:
179:Vertex figure
176:
172:
169:
165:
161:
157:
154:
150:
110:
108:
104:
100:
98:
94:
74:
70:
67:
64:
60:
57:
54:
50:
46:
41:
36:
31:
19:
18541:
18529:
18517:
18497:
18094:
17666:
17654:
17638:
17623:
17619:
17602:
17585:
17563:
17554:
17539:
17530:
17479:
17398:
17396:
17168:
17161:
17154:
17134:tessellation
17129:
17125:
17123:
16937:sr{4,4}×{∞}
16898:
16891:
16884:
16864:tessellation
16859:
16855:
16853:
16620:
16605:
16556:
16554:
16363:
16352:
16333:
16284:
16280:
16278:
16014:
15998:
15989:
15987:
15774:
15770:
15768:
15575:
15556:
15545:
15534:
15522:
15504:
15448:
15199:
15137:pmm (*2222)
15116:
15114:
15086:b-tCO-trille
15085:
15080:
15057:tessellation
15052:
15048:
15046:
14787:
14776:
14760:
14742:
14725:
14643:
14642:is called a
14639:
14637:
14607:
14545:pmm (*2222)
14524:
14522:
14475:1-RCO-trille
14474:
14469:
14416:
14377:
14373:
14371:
14099:
14088:
14076:
14062:
14049:
14038:
14027:
13966:
13964:
13679:
13596:
13584:
13580:
13578:
13279:
13268:
13252:
13234:
13195:
13178:
13095:
13094:is called a
13091:
13089:
12807:
12745:pmm (*2222)
12724:
12722:
12705:
12677:n-tCO-trille
12676:
12671:
12644:tessellation
12639:
12635:
12633:
12300:
12250:
12249:is called a
12246:
12244:
12214:cuboctahedra
12199:
11927:
11865:pmm (*2222)
11844:
11842:
11784:2-RCO-trille
11783:
11778:
11763:cuboctahedra
11751:tessellation
11746:
11742:
11740:
11189:
11085:
11081:
11079:
10652:
10638:
10626:
10616:
9702:
9612:pmm (*2222)
9579:
9577:
9551:
9543:
9538:
9487:tessellation
9480:
9190:
9179:
9168:
8878:
8816:pmm (*2222)
8795:
8793:
8776:
8767:
8762:
8739:tessellation
8734:
8730:
8728:
8413:
8398:
8318:
7715:
7653:pmm (*2222)
7632:
7630:
7613:
7604:
7599:
7592:square prism
7588:cuboctahedra
7576:tessellation
7571:
7567:
7565:
7463:square prism
5996:
5788:
5760:
5268:
5212:
5194:
5127:Quarter × 2
4521:
4338:
4325:
4319:
4308:
4300:
4290:
4032:
4016:Paracompact
3994:Euclidean E
3067:
2975:Paracompact
2920:
1743:Paracompact
1692:
1679:
1666:
1604:pmm (*2222)
1575:
1573:
845:
619:P4/mmm (123)
490:Rectangular
469:Rhombohedral
459:Orthorhombic
437:
421:
406:
397:circumsphere
374:
369:tessellation
367:
363:
359:
351:
345:
340:
305:tessellation
300:
296:
294:
17663:A. Andreini
17403:alternation
16626:symmetry).
16339:symmetry),
16019:Cell views
15951:tetrahedron
15841:tetrahedral
15779:alternation
15305:Space group
15134:p4m (*442)
15131:p6m (*632)
15111:Projections
14542:p4m (*442)
14539:p6m (*632)
14519:Projections
14325:Space group
14033:symmetry),
13602:symmetry),
12919:Space group
12742:p4m (*442)
12739:p6m (*632)
12719:Projections
12042:Space group
11862:p4m (*442)
11859:p6m (*632)
11839:Projections
11649:Space group
11204:Space group
10632:-symmetric
9772:Space group
9609:p4m (*442)
9606:p6m (*632)
9574:Projections
9566:cells with
9560:tetrahedron
9503:bitruncated
9497:made up of
9335:Edge figure
8990:Space group
8813:p4m (*442)
8810:p6m (*632)
8790:Projections
8772:pyramidille
8705:Pyramidille
8637:Space group
8381:symmetry .
7901:Space group
7650:p4m (*442)
7647:p6m (*632)
7627:Projections
7470:Space group
5580:↔ <>
5339:Honeycombs
4423:Honeycombs
4279:{3,∞}
4195:{∞,3}
4019:Noncompact
3920:{3,∞}
2978:Noncompact
2886:{∞,3}
1746:Noncompact
1601:p4m (*442)
1598:p6m (*632)
1570:Projections
861:Space group
635:P432 (207)
603:Space group
517:Point group
315:made up of
197:Space group
18578:Categories
17522:References
17467:tetrahedra
17385:Properties
17113:Properties
16935:s{4,4}×{∞}
16843:Properties
16543:Properties
16341:snub cubes
16267:Properties
15977:Properties
15825:snub cubes
15757:Properties
15571:tetrahedra
15559:snub cubes
15036:Properties
14768:tetrahedra
14361:Properties
14065:icosahedra
14035:icosahedra
13975:rectangles
13953:Properties
13604:tetrahedra
13593:icosahedra
13589:snub cubes
13567:Properties
13264:octahedron
13260:tetrahedra
13208:Two views
13176:symmetry.
12875:=<>
12623:Properties
12226:tetrahedra
11998:=<>
11730:Properties
11236:F23 (196)
11068:Properties
10664:rectangles
10649:tetrahedra
10569:Colored by
10562:(order 2)
10558:(order 1)
10554:(order 2)
10550:(order 4)
10546:(order 8)
9715:) for the
9457:Properties
9175:tetrahedra
8984:=<>
8718:Properties
8628:isosceles
7551:Properties
4322:tetrahedra
1695:octahedral
1669:4-polytope
877:honeycomb
621:P422 (89)
616:P222 (16)
464:Tetragonal
450:Monoclinic
387:, such as
356:polyhedral
327:. It is a
325:octahedron
280:Properties
190:octahedron
18502:honeycomb
18496:Uniform (
18073:Hexagonal
18006:−
17996:~
17960:~
17924:~
17891:−
17881:~
17848:−
17838:~
17805:−
17795:~
17762:−
17752:~
17584:, (2008)
17461:from the
17209:{4,4,2,∞}
17138:honeycomb
16868:honeycomb
16662:{4,4,2,∞}
16619:but with
16600:. It has
16351:but with
16328:. It has
15835:from the
15827:from the
15567:octahedra
15553:Dual cell
15338:Coloring
15326:Fibrifold
15278:~
15240:~
15128:Symmetry
15061:honeycomb
14994:~
14795:Dual cell
14749:octahedra
14702:~
14536:Symmetry
14386:honeycomb
14299:~
14107:Dual cell
14069:octahedra
14022:. It has
13977:from the
13320:sr{4,3,4}
13287:Dual cell
13155:~
13071:symmetry
12952:Coloring
12940:Fibrifold
12893:~
12853:~
12736:Symmetry
12648:honeycomb
12561:~
12222:octahedra
12206:octahedra
12181:symmetry
12137:Coloring
12016:~
11976:~
11856:Symmetry
11755:honeycomb
11688:~
11242:Fibrifold
11026:~
10706:2s{4,3,4}
10660:pentagons
10645:octahedra
10542:symmetry
10212:~
10144:~
10071:=<>
10048:~
9952:~
9854:~
9814:Fibrifold
9730:~
9603:Symmetry
9491:honeycomb
9412:~
9246:2t{4,3,4}
9198:Dual cell
9171:octahedra
9010:Coloring
8962:~
8924:~
8807:Symmetry
8751:octahedra
8743:honeycomb
8675:~
8601:Face type
8577:Cell type
8421:Dual cell
8401:octahedra
8280:order 16
8269:symmetry
7943:Coloring
7875:~
7836:~
7797:~
7758:~
7644:Symmetry
7584:octahedra
7580:honeycomb
7508:~
7015:~
6977:~
6895:~
6857:~
6720:~
6679:~
6592:<2>
6518:~
6327:~
6286:~
6161:~
6063:Fibrifold
6016:~
5725:<>
5320:Fibrifold
5042:Half × 2
4404:Fibrifold
4316:Dual cell
1672:tesseract
1595:Symmetry
626:R3 (146)
624:R3m (160)
614:Pmmm (47)
481:Unit cell
454:Triclinic
377:Euclidean
335:{4,3,4}.
329:self-dual
309:honeycomb
267:self-dual
235:~
167:Face type
152:Cell type
72:Indexing
17484:See also
17377:Symmetry
17352:triangle
17215:{4,4,∞}
17074:triangle
16668:{4,4,∞}
16488:triangle
16405:{4,3,4}
16221:triangle
16120:{4,3,4}
15958:Symmetry
15876:{4,3,4}
15738:Symmetry
15708:triangle
15620:{4,3,4}
15320:m (229)
15222:Symmetry
15196:Symmetry
14832:{4,3,4}
14241:triangle
14144:{4,3,4}
13905:triangle
13813:{4,3,4}
13476:triangle
13322:sr{4,3}
13079:order 1
13075:order 2
12934:m (225)
12804:Symmetry
12347:tr{4,3}
12189:order 1
12185:order 2
11924:Symmetry
11482:rr{4,3}
11441:quarter
10987:triangle
9808:m (227)
9801:3m (216)
9699:Symmetry
9520:, it is
9252:{4,3,4}
8875:Symmetry
8605:triangle
8313:order 4
8302:order 8
8291:order 8
7739:Symmetry
7712:Symmetry
7439:triangle
6209:<>
6086:Extended
6083:diagram
6081:Extended
6077:symmetry
6075:Extended
6070:symmetry
5578:<>
5333:diagram
5331:Extended
5327:symmetry
5325:Extended
4417:diagram
4415:Extended
4411:symmetry
4409:Extended
4383:expanded
4013:Compact
2972:Compact
1740:Compact
1217:{4,3,4}
1191:m (229)
1170:{4,3,4}
1124:m (221)
1034:m (225)
1013:{4,3,4}
890:m (221)
562:Diagram
557:, (432)
555:Order 48
553:, (*432)
543:, (422)
541:Order 16
539:, (*422)
536:, (222)
532:, (*222)
502:Trigonal
101:{4,3,4}
18539:qδ
18527:hδ
18482:qδ
18474:hδ
18443:qδ
18435:hδ
18382:qδ
18373:hδ
18321:qδ
18311:hδ
18266:qδ
18256:hδ
18217:qδ
18207:hδ
18165:qδ
18155:hδ
18116:qδ
18106:hδ
18064:qδ
18054:hδ
17718:regular
17547:A000029
17213:0,1,2,3
16810:octagon
16666:0,1,2,3
15874:0,1,2,3
15618:0,1,2,3
15472:4.8.4.8
15463:4.4.4.6
15313:m (221)
14964:m (229)
14921:octagon
14916:hexagon
14887:tr{4,3}
14830:0,1,2,3
14646:, with
14465:regular
14409:pyramid
14337:m (221)
14273:pyramid
14251:octagon
14199:rr{4,3}
13098:, with
12927:m (221)
12613:Cells:
12599:m (221)
12511:octagon
12506:hexagon
12468:tr{4,3}
12345:{4,3,4}
12232:with a
11661:m (221)
11603:rr{4,3}
11480:{4,3,4}
11438:double
11436:quarter
11427:double
10708:2s{4,3}
10452:1:1:1:1
9794:m (225)
9787:m (221)
9780:m (229)
9570:faces.
9546:in his
9383:m (229)
9327:hexagon
8649:m (221)
8610:octagon
8460:t{4,3}
8458:{4,3,4}
8331:. This
8325:hexagon
7979:diagram
7977:Coxeter
7732:below.
7482:m (221)
7104:2r{4,3}
7100:{4,3,4}
6184:(None)
4203:figure
4053:{8,3,8}
4048:{7,3,7}
4043:{6,3,6}
4038:{5,3,5}
4033:{4,3,4}
4028:{3,3,3}
4010:Affine
4007:Finite
3377:{4,3,8}
3334:{4,3,7}
3225:{4,3,6}
3182:{4,3,5}
3068:{4,3,4}
3025:{4,3,3}
2969:Affine
2966:Finite
2272:{8,3,4}
2201:{7,3,4}
2054:{6,3,4}
1983:{5,3,4}
1826:{4,3,4}
1755:{3,3,4}
1737:Affine
1734:Finite
875:Partial
633:m (221)
611:P1 (1)
550:, (33)
548:Order 6
546:, (*33)
534:Order 8
527:Order 2
496:Square
430:cells.
411:, with
341:cubille
288:regular
209:m (221)
18515:δ
18466:δ
18427:δ
18363:δ
18301:δ
18246:δ
18197:δ
18145:δ
18096:δ
18044:δ
17734:Family
17730:Space
17645:
17611:
17592:
17357:square
17328:s{2,4}
17103:Cell:
17079:square
17059:{}x{3}
17050:{}x{4}
16833:Cell:
16805:square
16790:{}x{4}
16781:{}x{8}
16604:(with
16533:Cell:
16493:square
16473:{}x{4}
16332:(with
16257:Cell:
16226:square
16206:{}x{3}
16197:{}x{4}
16188:s{4,3}
15713:square
15684:s{2,4}
15675:s{4,3}
15299:×2, ]
15168:Frame
15142:Solid
15101:
14911:square
14896:{}x{8}
14759:(both
14576:Frame
14550:Solid
14400:, and
14246:square
14226:{}x{4}
14217:{}x{8}
14208:t{4,3}
14037:(with
14026:(with
13943:Cell:
13910:square
13890:{}x{3}
13881:s{3,3}
13595:(with
13557:Cell:
13481:square
13452:s{3,3}
13443:s{4,3}
13069:figure
13067:Vertex
12776:Frame
12750:Solid
12702:Images
12692:
12658:, and
12501:square
12486:{}x{4}
12477:t{3,4}
12179:figure
12177:Vertex
11896:Frame
11870:Solid
11808:Images
11765:, and
11720:Cell:
11621:{}x{4}
11612:r{4,3}
11424:Order
11159:, and
11058:Cell:
10972:s{3,3}
10710:sr{3}
10540:figure
10538:Vertex
10167:
9657:Frame
9617:Solid
9447:Cell:
9322:square
9307:t{3,4}
9221:
8847:Frame
8821:Solid
8708:Cell:
8581:t{4,3}
8289:(*222)
8278:(*224)
8267:figure
8265:Vertex
7938:(216)
7724:, and
7684:Frame
7658:Solid
7541:Cell:
7444:square
7415:r{4,3}
7102:r{4,3}
7056:
6952:(229)
6936:
6785:(204)
6770:
6578:(221)
6562:
6427:(227)
6411:
6377:
6195:(225)
6102:(216)
6088:group
6068:Square
5719:(221)
5572:(225)
5350:(225)
5336:Order
5269:The ,
5163:(229)
5078:(227)
5014:(217)
4752:(225)
4434:(221)
4420:Order
4339:The ,
4201:Vertex
4119:Cells
4065:Image
3986:Space
3588:figure
3586:Vertex
3531:Image
2943:Space
2642:Cells
2588:Image
1711:Space
1635:Frame
1609:Solid
1104:{4,3}
609:Pm (6)
529:, (1)
498:cuboid
492:cuboid
426:using
364:tiling
270:Cell:
171:square
62:Family
17516:Voxel
17471:cubes
17348:Faces
17337:{3,3}
17324:Cells
17207:1,2,3
17146:cubes
17140:) in
17070:Faces
17046:Cells
16880:cubes
16870:) in
16801:Faces
16777:Cells
16660:0,1,3
16613:cubes
16484:Faces
16464:{3,4}
16456:Cells
16345:cubes
16217:Faces
16179:{3,4}
16171:Cells
15704:Faces
15693:{3,3}
15671:Cells
15519:cubes
15026:Cell
14907:Faces
14883:Cells
14753:cubes
14402:cubes
14351:Cell
14237:Faces
14195:Cells
14142:0,1,3
13979:cubes
13901:Faces
13872:{3,4}
13864:Cells
13472:Faces
13461:{3,3}
13439:Cells
13245:cubes
13200:with
12660:cubes
12497:Faces
12464:Cells
12343:0,1,2
12257:with
11771:wedge
11767:cubes
11642:wedge
11599:Cells
11433:half
11430:full
11233:(203)
11226:(202)
11219:(200)
11212:(204)
10983:Faces
10963:{3,3}
10959:Cells
10571:cell
10567:Image
10431:2:1:1
9493:) in
9318:Faces
9303:Cells
8590:{3,4}
8311:(*22)
8300:(*44)
7929:(225)
7920:(225)
7911:(221)
7435:Faces
7424:{3,4}
7411:Cells
7106:r{3}
6443:or ]
6058:group
6056:Space
5315:group
5313:Space
4830:Half
4399:group
4397:Space
4297:cubes
4293:cubes
4268:{3,8}
4257:{3,7}
4246:{3,6}
4235:{3,5}
4224:{3,4}
4213:{3,3}
4184:{8,3}
4173:{7,3}
4162:{6,3}
4151:{5,3}
4140:{4,3}
4129:{3,3}
4024:Name
4004:Form
3858:{3,8}
3819:{3,7}
3762:{3,6}
3723:{3,5}
3666:{3,4}
3627:{3,3}
2963:Form
2930:cells
2927:cubic
2847:{8,3}
2808:{7,3}
2769:{6,3}
2730:{5,3}
2691:{4,3}
2652:{3,3}
1751:Name
1731:Form
525:, (*)
520:Order
474:Cubic
360:cells
350:is a
317:cubic
311:) in
156:{4,3}
77:11,15
18500:-1)-
17720:and
17643:ISBN
17609:ISBN
17590:ISBN
17359:{4}
17190:Type
17148:and
17136:(or
17124:The
17096:Dual
17081:{4}
16920:Type
16878:and
16866:(or
16854:The
16826:Dual
16812:{8}
16643:Type
16617:cube
16555:The
16530:Dual
16495:{4}
16386:Type
16362:(as
16349:cube
16279:The
16254:Dual
16228:{4}
16101:Type
16030:Net
15967:Dual
15927:Cell
15859:Type
15747:Dual
15715:{4}
15601:Type
15333:8:2
15208:and
15115:The
15067:and
15059:(or
15047:The
15019:Dual
14923:{8}
14813:Type
14523:The
14384:(or
14372:The
14344:Dual
14339:4:2
14253:{8}
14125:Type
14075:(as
14048:(as
13965:The
13940:Dual
13912:{4}
13794:Type
13579:The
13516:Dual
13483:{4}
13305:Type
13251:(as
12947:2:2
12723:The
12646:(or
12634:The
12606:Dual
12601:4:2
12513:{8}
12326:Type
12253:, a
12230:cube
11843:The
11753:(or
11741:The
11713:Dual
11663:4:2
11461:Type
11080:The
11051:Dual
10989:{3}
10691:Type
10666:, 4
10662:, 4
10621:and
9830:2:2
9758:and
9578:The
9489:(or
9481:The
9438:Dual
9342:{3}
9329:{6}
9231:Type
8794:The
8749:and
8741:(or
8729:The
8701:Dual
8651:4:2
8612:{8}
8439:Type
7631:The
7586:and
7578:(or
7566:The
7534:Dual
7484:4:2
7446:{4}
7081:Type
6960:↔ ]
6955:8:2
6801:↔ ]
6581:4:2
6430:2:2
6198:2:2
6105:1:2
5722:4:2
5575:2:2
5353:2:2
5240:,
5166:8:2
5086:↔ ]
5081:2:2
5017:4:2
4755:2:2
4437:4:2
3452:...
2983:Name
2428:...
1574:The
510:Cube
307:(or
295:The
262:Dual
211:4:2
173:{4}
52:Type
17354:{3}
17128:or
17076:{3}
16858:or
16807:{4}
16490:{3}
16403:0,3
16283:or
16223:{3}
15872:dht
15773:or
15769:An
15710:{3}
15330:4:2
15261:,
15051:or
14967:8:2
14918:{6}
14913:{4}
14376:or
14248:{4}
14243:{3}
13907:{3}
13639:or
13583:or
13478:{3}
12944:4:2
12638:or
12508:{6}
12503:{4}
11745:or
11478:0,2
11084:or
11011:],
10479:1:1
10416:1:1
9827:1:2
9824:2:2
9821:4:2
9818:8:2
9594:.
9433:,
9386:8:2
9324:{4}
9250:1,2
8733:or
8696:,
8607:{3}
8456:0,1
7570:or
7529:,
7441:{3}
7036:×2
6939:(*)
6916:×2
6880:↔ ½
6791:r8
6594:↔
6584:d4
6433:g2
6211:↔
6201:d2
6108:a1
6044::
5889:(6)
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