113:
132:
91:
75:
34:
102:
63:
45:
259:
used to characterise polyhedra does not generalize usefully to higher dimensions, and is zero for all 6-polytopes, whatever their underlying topology. This inadequacy of the Euler characteristic to reliably distinguish between different topologies in higher dimensions led to the discovery of the more
404:
into a regular grid of 5-polytope facets. Strictly speaking, tessellations are not 6-polytopes as they do not bound a "6D" volume, but we include them here for the sake of completeness because they are similar in many ways to 6-polytope. A
289:
if its boundary (including its 5-faces, 4-faces, cells, faces and edges) does not intersect itself and the line segment joining any two points of the 6-polytope is contained in the 6-polytope or its interior; otherwise, it is
263:
Similarly, the notion of orientability of a polyhedron is insufficient to characterise the surface twistings of toroidal polytopes, and this led to the use of torsion coefficients.
1502:
1653:
1086:
1394:
1750:
1725:
1688:
1658:
1641:
1616:
1611:
1546:
1531:
1414:
1331:
1306:
1283:
1134:
1091:
1040:
1005:
950:
900:
733:
637:
543:
1765:
1755:
1693:
1631:
1621:
1561:
1551:
1522:
1512:
1492:
1482:
1434:
1424:
1404:
1301:
1000:
1745:
1735:
1683:
1673:
1663:
1541:
1341:
1321:
1311:
1293:
1273:
1263:
1253:
1243:
1184:
1174:
1164:
1154:
1144:
1126:
1116:
1106:
1096:
1030:
1020:
1010:
940:
930:
920:
910:
783:
773:
763:
753:
743:
687:
677:
667:
657:
647:
593:
583:
573:
563:
553:
1760:
1636:
1626:
1556:
1517:
1507:
1497:
1487:
1429:
1419:
1409:
1399:
1740:
1730:
1678:
1668:
1536:
1336:
1326:
1316:
1288:
1278:
1268:
1258:
1248:
1179:
1169:
1159:
1149:
1139:
1121:
1111:
1101:
1035:
1025:
1015:
945:
935:
925:
915:
905:
778:
768:
758:
748:
738:
682:
672:
662:
652:
642:
588:
578:
568:
558:
548:
21:
2538:
1874:
1973:
1837:, Verhandelingen of the Koninklijke academy van Wetenschappen width unit Amsterdam, Eerste Sectie 11,1, Amsterdam, 1910
1946:
1904:
1840:
249:
450:
316:
378:
of two lower-dimensional polytopes. A prismatic 6-polytope is uniform if its factors are uniform. The
390:), but is considered separately because it has symmetries other than those inherited from its factors.
1877:
1996:
1824:
301:
1966:
848:
495:
2510:
2503:
2496:
1222:
711:
148:
106:
2035:
2013:
2001:
2555:
2167:
2114:
1646:
324:
256:
136:
79:
8:
2522:
2421:
2171:
1604:
439:
170:
1916:
2391:
2341:
2291:
2248:
2218:
2178:
2141:
1959:
1830:
885:
823:
414:
364:
352:
330:
194:
95:
25:
841:
488:
431:
2530:
1870:
383:
375:
182:
2534:
2099:
2088:
2077:
2066:
2057:
2048:
1987:
1983:
1930:
1702:
198:
2124:
2109:
443:
401:
356:
285:
190:
186:
2474:
1935:
1866:
1816:
1714:
877:
524:
348:
311:
has all identical regular 5-polytope facets. All regular 6-polytope are convex.
17:
1941:
1869:, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
1835:
Geometrical deduction of semiregular from regular polytopes and space fillings
2549:
2491:
2379:
2372:
2365:
2329:
2322:
2315:
2279:
2272:
1600:
1467:
1379:
873:
520:
427:
334:
295:
2431:
396:
245:
202:
235:
The figure is not a compound of other figures which meet the requirements.
2440:
2401:
2351:
2301:
2258:
2228:
2160:
2146:
1850:, Philosophical Transactions of the Royal Society of London, Londne, 1954
983:
626:
470:
410:
49:
2426:
2410:
2360:
2310:
2267:
2237:
2151:
1073:
272:
229:
218:
214:
210:
167:
117:
2482:
2396:
2346:
2296:
2253:
2223:
2192:
532:
458:
38:
2456:
2211:
2207:
2134:
276:
163:
151:
112:
476:
There are no nonconvex regular polytopes of 5 or more dimensions.
2465:
2435:
2202:
2197:
2188:
2129:
206:
1821:
On the
Regular and Semi-Regular Figures in Space of n Dimensions
131:
90:
74:
2405:
2355:
2305:
2262:
2232:
2183:
2119:
722:
464:
379:
67:
33:
1806:
Euler's Gem: The
Polyhedron Formula and the Birth of Topoplogy
828:
Here are six simple uniform convex 6-polytopes, including the
479:
For the three convex regular 6-polytopes, their elements are:
351:
under which all vertices are equivalent, and its facets are
101:
62:
44:
2155:
387:
300:, from analogy with the star-like shapes of the non-convex
1846:
H.S.M. Coxeter, M.S. Longuet-Higgins und J.C.P. Miller:
244:
The topology of any given 6-polytope is defined by its
221:. Furthermore, the following requirements must be met:
228:
Adjacent facets are not in the same five-dimensional
181:
A 6-polytope is a closed six-dimensional figure with
225:
Each 4-face must join exactly two 5-faces (facets).
1863:Kaleidoscopes: Selected Writings of H.S.M. Coxeter
271:6-polytopes may be classified by properties like "
1911:, Ph.D. Dissertation, University of Toronto, 1966
294:. Self-intersecting 6-polytope are also known as
2547:
205:where four or more faces meet, and a face is a
197:(3-faces), 4-faces, and 5-faces. A vertex is a
1909:The Theory of Uniform Polytopes and Honeycombs
333:facets. There is only one such figure, called
1967:
209:where three or more cells meet. A cell is a
201:where six or more edges meet. An edge is a
1974:
1960:
1800:
1798:
1796:
832:repeated with its alternate construction.
426:Regular 6-polytopes can be generated from
355:. The faces of a uniform polytope must be
15:
317:List of regular polytopes § Convex_5
87:
30:
2539:List of regular polytopes and compounds
1793:
409:is one whose vertices are related by a
2548:
1897:Regular and Semi-Regular Polytopes III
817:
421:
1890:Regular and Semi-Regular Polytopes II
1914:
1883:Regular and Semi Regular Polytopes I
400:is the division of five-dimensional
1857:, 3rd Edition, Dover New York, 1973
13:
1776:polytope is the vertex figure and
239:
14:
2567:
1924:
1917:"6D uniform polytopes (polypeta)"
266:
1763:
1758:
1753:
1748:
1743:
1738:
1733:
1728:
1723:
1691:
1686:
1681:
1676:
1671:
1666:
1661:
1656:
1651:
1639:
1634:
1629:
1624:
1619:
1614:
1609:
1559:
1554:
1549:
1544:
1539:
1534:
1529:
1520:
1515:
1510:
1505:
1500:
1495:
1490:
1485:
1480:
1432:
1427:
1422:
1417:
1412:
1407:
1402:
1397:
1392:
1339:
1334:
1329:
1324:
1319:
1314:
1309:
1304:
1299:
1291:
1286:
1281:
1276:
1271:
1266:
1261:
1256:
1251:
1246:
1241:
1182:
1177:
1172:
1167:
1162:
1157:
1152:
1147:
1142:
1137:
1132:
1124:
1119:
1114:
1109:
1104:
1099:
1094:
1089:
1084:
1038:
1033:
1028:
1023:
1018:
1013:
1008:
1003:
998:
948:
943:
938:
933:
928:
923:
918:
913:
908:
903:
898:
781:
776:
771:
766:
761:
756:
751:
746:
741:
736:
731:
685:
680:
675:
670:
665:
660:
655:
650:
645:
640:
635:
591:
586:
581:
576:
571:
566:
561:
556:
551:
546:
541:
130:
111:
100:
89:
73:
61:
43:
32:
1936:Polytopes of Various Dimensions
329:contains two or more types of
1:
1865:, edited by F. Arthur Sherk,
1786:
260:sophisticated Betti numbers.
176:
1465:
1377:
1220:
1071:
981:
883:
720:
624:
530:
407:uniform 5-space tessellation
7:
1895:(Paper 24) H.S.M. Coxeter,
1888:(Paper 23) H.S.M. Coxeter,
1881:(Paper 22) H.S.M. Coxeter,
382:is prismatic (product of a
10:
2572:
2528:
1955:
1942:Multi-dimensional Glossary
821:
451:convex regular 6-polytopes
449:There are only three such
362:
314:
1825:Messenger of Mathematics
991:(alternate construction)
302:Kepler-Poinsot polyhedra
156:six-dimensional polytope
1947:Glossary for hyperspace
374:is constructed by the
1699:rectified 6-orthoplex
1697:, vertex figure is a
1223:Rectified 6-orthoplex
438:{p,q,r,s} 5-polytope
413:and whose facets are
107:Rectified 6-orthoplex
1647:6-demicube honeycomb
372:prismatic 6-polytope
257:Euler characteristic
250:torsion coefficients
217:, and a 5-face is a
2523:pentagonal polytope
2422:Uniform 10-polytope
1982:Fundamental convex
1949:, George Olshevsky.
1915:Klitzing, Richard.
1605:6-simplex honeycomb
818:Uniform 6-polytopes
430:represented by the
422:Regular 6-polytopes
415:uniform 5-polytopes
353:uniform 5-polytopes
28:
26:Uniform 6-polytopes
2392:Uniform 9-polytope
2342:Uniform 8-polytope
2292:Uniform 7-polytope
2249:Uniform 6-polytope
2219:Uniform 5-polytope
2179:Uniform polychoron
2142:Uniform polyhedron
1990:in dimensions 2–10
1808:, Princeton, 2008.
1597:expanded 6-simplex
886:Expanded 6-simplex
824:Uniform 6-polytope
365:Uniform 6-polytope
345:uniform 6-polytope
331:regular 4-polytope
309:regular 6-polytope
96:Expanded 6-simplex
16:
2544:
2543:
2531:Polytope families
1988:uniform polytopes
1938:, Jonathan Bowers
1875:978-0-471-01003-6
1855:Regular Polytopes
1848:Uniform Polyhedra
1827:, Macmillan, 1900
1593:
1592:
815:
814:
434:{p,q,r,s,t} with
376:Cartesian product
255:The value of the
145:
144:
2563:
2535:Regular polytope
2096:
2085:
2074:
2033:
1976:
1969:
1962:
1953:
1952:
1920:
1853:H.S.M. Coxeter,
1809:
1802:
1768:
1767:
1766:
1762:
1761:
1757:
1756:
1752:
1751:
1747:
1746:
1742:
1741:
1737:
1736:
1732:
1731:
1727:
1726:
1696:
1695:
1694:
1690:
1689:
1685:
1684:
1680:
1679:
1675:
1674:
1670:
1669:
1665:
1664:
1660:
1659:
1655:
1654:
1644:
1643:
1642:
1638:
1637:
1633:
1632:
1628:
1627:
1623:
1622:
1618:
1617:
1613:
1612:
1564:
1563:
1562:
1558:
1557:
1553:
1552:
1548:
1547:
1543:
1542:
1538:
1537:
1533:
1532:
1525:
1524:
1523:
1519:
1518:
1514:
1513:
1509:
1508:
1504:
1503:
1499:
1498:
1494:
1493:
1489:
1488:
1484:
1483:
1437:
1436:
1435:
1431:
1430:
1426:
1425:
1421:
1420:
1416:
1415:
1411:
1410:
1406:
1405:
1401:
1400:
1396:
1395:
1344:
1343:
1342:
1338:
1337:
1333:
1332:
1328:
1327:
1323:
1322:
1318:
1317:
1313:
1312:
1308:
1307:
1303:
1302:
1296:
1295:
1294:
1290:
1289:
1285:
1284:
1280:
1279:
1275:
1274:
1270:
1269:
1265:
1264:
1260:
1259:
1255:
1254:
1250:
1249:
1245:
1244:
1187:
1186:
1185:
1181:
1180:
1176:
1175:
1171:
1170:
1166:
1165:
1161:
1160:
1156:
1155:
1151:
1150:
1146:
1145:
1141:
1140:
1136:
1135:
1129:
1128:
1127:
1123:
1122:
1118:
1117:
1113:
1112:
1108:
1107:
1103:
1102:
1098:
1097:
1093:
1092:
1088:
1087:
1043:
1042:
1041:
1037:
1036:
1032:
1031:
1027:
1026:
1022:
1021:
1017:
1016:
1012:
1011:
1007:
1006:
1002:
1001:
953:
952:
951:
947:
946:
942:
941:
937:
936:
932:
931:
927:
926:
922:
921:
917:
916:
912:
911:
907:
906:
902:
901:
835:
834:
786:
785:
784:
780:
779:
775:
774:
770:
769:
765:
764:
760:
759:
755:
754:
750:
749:
745:
744:
740:
739:
735:
734:
690:
689:
688:
684:
683:
679:
678:
674:
673:
669:
668:
664:
663:
659:
658:
654:
653:
649:
648:
644:
643:
639:
638:
596:
595:
594:
590:
589:
585:
584:
580:
579:
575:
574:
570:
569:
565:
564:
560:
559:
555:
554:
550:
549:
545:
544:
482:
481:
297:star 6-polytopes
283:A 6-polytope is
213:. A 4-face is a
134:
115:
104:
93:
77:
65:
47:
36:
29:
2571:
2570:
2566:
2565:
2564:
2562:
2561:
2560:
2546:
2545:
2514:
2507:
2500:
2383:
2376:
2369:
2333:
2326:
2319:
2283:
2276:
2110:Regular polygon
2103:
2094:
2087:
2083:
2076:
2072:
2063:
2054:
2047:
2043:
2031:
2025:
2021:
2009:
1991:
1980:
1927:
1813:
1812:
1803:
1794:
1789:
1781:
1774:
1764:
1759:
1754:
1749:
1744:
1739:
1734:
1729:
1724:
1722:
1718:
1692:
1687:
1682:
1677:
1672:
1667:
1662:
1657:
1652:
1650:
1640:
1635:
1630:
1625:
1620:
1615:
1610:
1608:
1603:of the uniform
1588:
1560:
1555:
1550:
1545:
1540:
1535:
1530:
1528:
1526:
1521:
1516:
1511:
1506:
1501:
1496:
1491:
1486:
1481:
1479:
1471:
1461:
1433:
1428:
1423:
1418:
1413:
1408:
1403:
1398:
1393:
1391:
1383:
1374:
1370:
1368:
1340:
1335:
1330:
1325:
1320:
1315:
1310:
1305:
1300:
1298:
1297:
1292:
1287:
1282:
1277:
1272:
1267:
1262:
1257:
1252:
1247:
1242:
1240:
1236:
1232:
1230:
1217:
1213:
1211:
1183:
1178:
1173:
1168:
1163:
1158:
1153:
1148:
1143:
1138:
1133:
1131:
1130:
1125:
1120:
1115:
1110:
1105:
1100:
1095:
1090:
1085:
1083:
1079:
1067:
1039:
1034:
1029:
1024:
1019:
1014:
1009:
1004:
999:
997:
990:
989:
977:
949:
944:
939:
934:
929:
924:
919:
914:
909:
904:
899:
897:
893:
850:
843:
826:
820:
810:
782:
777:
772:
767:
762:
757:
752:
747:
742:
737:
732:
730:
715:
686:
681:
676:
671:
666:
661:
656:
651:
646:
641:
636:
634:
620:
592:
587:
582:
577:
572:
567:
562:
557:
552:
547:
542:
540:
497:
490:
432:Schläfli symbol
424:
402:Euclidean space
367:
338:
319:
269:
242:
240:Characteristics
179:
149:six-dimensional
140:
135:
127:(Demihexeract)
126:
124:
116:
105:
94:
83:
78:
66:
57:
48:
37:
12:
11:
5:
2569:
2559:
2558:
2542:
2541:
2526:
2525:
2516:
2512:
2505:
2498:
2494:
2485:
2468:
2459:
2448:
2447:
2445:
2443:
2438:
2429:
2424:
2418:
2417:
2415:
2413:
2408:
2399:
2394:
2388:
2387:
2385:
2381:
2374:
2367:
2363:
2358:
2349:
2344:
2338:
2337:
2335:
2331:
2324:
2317:
2313:
2308:
2299:
2294:
2288:
2287:
2285:
2281:
2274:
2270:
2265:
2256:
2251:
2245:
2244:
2242:
2240:
2235:
2226:
2221:
2215:
2214:
2205:
2200:
2195:
2186:
2181:
2175:
2174:
2165:
2163:
2158:
2149:
2144:
2138:
2137:
2132:
2127:
2122:
2117:
2112:
2106:
2105:
2101:
2097:
2092:
2081:
2070:
2061:
2052:
2045:
2039:
2029:
2023:
2017:
2011:
2005:
1999:
1993:
1992:
1981:
1979:
1978:
1971:
1964:
1956:
1951:
1950:
1944:
1939:
1933:
1931:Polytope names
1926:
1925:External links
1923:
1922:
1921:
1912:
1902:
1901:
1900:
1893:
1886:
1867:Peter McMullen
1860:
1859:
1858:
1851:
1841:H.S.M. Coxeter
1838:
1831:A. Boole Stott
1828:
1811:
1810:
1804:Richeson, D.;
1791:
1790:
1788:
1785:
1779:
1772:
1716:
1713:. The uniform
1591:
1590:
1586:
1583:
1580:
1577:
1574:
1571:
1568:
1565:
1477:
1474:
1469:
1464:
1463:
1459:
1456:
1453:
1450:
1447:
1444:
1441:
1438:
1389:
1386:
1381:
1376:
1375:
1372:
1366:
1363:
1360:
1357:
1354:
1351:
1348:
1345:
1238:
1234:
1228:
1225:
1219:
1218:
1215:
1209:
1206:
1203:
1200:
1197:
1194:
1191:
1188:
1081:
1076:
1070:
1069:
1065:
1062:
1059:
1056:
1053:
1050:
1047:
1044:
995:
992:
987:
980:
979:
975:
972:
969:
966:
963:
960:
957:
954:
895:
891:
888:
882:
881:
871:
868:
865:
862:
859:
856:
853:
846:
839:
822:Main article:
819:
816:
813:
812:
808:
805:
802:
799:
796:
793:
790:
787:
728:
725:
719:
718:
713:
709:
706:
703:
700:
697:
694:
691:
632:
629:
623:
622:
618:
615:
612:
609:
606:
603:
600:
597:
538:
535:
529:
528:
518:
515:
512:
509:
506:
503:
500:
493:
486:
474:
473:
469:{3,3,3,3,4} -
467:
463:{4,3,3,3,3} -
461:
457:{3,3,3,3,3} -
428:Coxeter groups
423:
420:
419:
418:
391:
363:Main article:
361:
360:
349:symmetry group
341:
336:
315:Main article:
313:
312:
305:
268:
267:Classification
265:
241:
238:
237:
236:
233:
226:
178:
175:
143:
142:
138:
128:
122:
109:
98:
86:
85:
81:
71:
59:
55:
41:
9:
6:
4:
3:
2:
2568:
2557:
2554:
2553:
2551:
2540:
2536:
2532:
2527:
2524:
2520:
2517:
2515:
2508:
2501:
2495:
2493:
2489:
2486:
2484:
2480:
2476:
2472:
2469:
2467:
2463:
2460:
2458:
2454:
2450:
2449:
2446:
2444:
2442:
2439:
2437:
2433:
2430:
2428:
2425:
2423:
2420:
2419:
2416:
2414:
2412:
2409:
2407:
2403:
2400:
2398:
2395:
2393:
2390:
2389:
2386:
2384:
2377:
2370:
2364:
2362:
2359:
2357:
2353:
2350:
2348:
2345:
2343:
2340:
2339:
2336:
2334:
2327:
2320:
2314:
2312:
2309:
2307:
2303:
2300:
2298:
2295:
2293:
2290:
2289:
2286:
2284:
2277:
2271:
2269:
2266:
2264:
2260:
2257:
2255:
2252:
2250:
2247:
2246:
2243:
2241:
2239:
2236:
2234:
2230:
2227:
2225:
2222:
2220:
2217:
2216:
2213:
2209:
2206:
2204:
2201:
2199:
2198:Demitesseract
2196:
2194:
2190:
2187:
2185:
2182:
2180:
2177:
2176:
2173:
2169:
2166:
2164:
2162:
2159:
2157:
2153:
2150:
2148:
2145:
2143:
2140:
2139:
2136:
2133:
2131:
2128:
2126:
2123:
2121:
2118:
2116:
2113:
2111:
2108:
2107:
2104:
2098:
2095:
2091:
2084:
2080:
2073:
2069:
2064:
2060:
2055:
2051:
2046:
2044:
2042:
2038:
2028:
2024:
2022:
2020:
2016:
2012:
2010:
2008:
2004:
2000:
1998:
1995:
1994:
1989:
1985:
1977:
1972:
1970:
1965:
1963:
1958:
1957:
1954:
1948:
1945:
1943:
1940:
1937:
1934:
1932:
1929:
1928:
1918:
1913:
1910:
1906:
1903:
1898:
1894:
1891:
1887:
1884:
1880:
1879:
1878:
1876:
1872:
1868:
1864:
1861:
1856:
1852:
1849:
1845:
1844:
1842:
1839:
1836:
1832:
1829:
1826:
1822:
1818:
1815:
1814:
1807:
1801:
1799:
1797:
1792:
1784:
1782:
1775:
1720:
1712:
1708:
1704:
1700:
1648:
1606:
1602:
1601:vertex figure
1598:
1584:
1581:
1578:
1575:
1572:
1569:
1566:
1478:
1475:
1473:
1466:
1457:
1454:
1451:
1448:
1445:
1442:
1439:
1390:
1387:
1385:
1378:
1364:
1361:
1358:
1355:
1352:
1349:
1346:
1239:
1226:
1224:
1221:
1207:
1204:
1201:
1198:
1195:
1192:
1189:
1082:
1077:
1075:
1072:
1063:
1060:
1057:
1054:
1051:
1048:
1045:
996:
993:
985:
982:
973:
970:
967:
964:
961:
958:
955:
896:
889:
887:
884:
879:
875:
872:
869:
866:
863:
860:
857:
854:
852:
847:
845:
840:
837:
836:
833:
831:
825:
806:
803:
800:
797:
794:
791:
788:
729:
726:
724:
721:
716:
710:
707:
704:
701:
698:
695:
692:
633:
630:
628:
625:
616:
613:
610:
607:
604:
601:
598:
539:
536:
534:
531:
526:
522:
519:
516:
513:
510:
507:
504:
501:
499:
494:
492:
487:
484:
483:
480:
477:
472:
468:
466:
462:
460:
456:
455:
454:
452:
447:
445:
441:
437:
433:
429:
416:
412:
408:
403:
399:
398:
392:
389:
385:
381:
377:
373:
369:
368:
366:
358:
354:
350:
346:
342:
339:
332:
328:
326:
321:
320:
318:
310:
306:
303:
299:
298:
293:
288:
287:
282:
281:
280:
278:
274:
264:
261:
258:
253:
251:
247:
246:Betti numbers
234:
231:
227:
224:
223:
222:
220:
216:
212:
208:
204:
200:
196:
192:
188:
184:
174:
172:
169:
166:, bounded by
165:
161:
157:
153:
150:
141:
133:
129:
125:
119:
114:
110:
108:
103:
99:
97:
92:
88:
84:
76:
72:
69:
64:
60:
58:
51:
46:
42:
40:
35:
31:
27:
23:
19:
2518:
2487:
2478:
2470:
2461:
2452:
2432:10-orthoplex
2168:Dodecahedron
2089:
2078:
2067:
2058:
2049:
2040:
2036:
2026:
2018:
2014:
2006:
2002:
1908:
1905:N.W. Johnson
1896:
1889:
1882:
1862:
1854:
1847:
1834:
1820:
1805:
1777:
1770:
1710:
1706:
1698:
1596:
1594:
1080:h{4,3,3,3,3}
829:
827:
478:
475:
448:
442:around each
435:
425:
406:
397:tessellation
394:
371:
344:
325:semi-regular
323:
308:
296:
291:
284:
270:
262:
254:
243:
203:line segment
180:
159:
155:
146:
120:
53:
2556:6-polytopes
2441:10-demicube
2402:9-orthoplex
2352:8-orthoplex
2302:7-orthoplex
2259:6-orthoplex
2229:5-orthoplex
2184:Pentachoron
2172:Icosahedron
2147:Tetrahedron
1707:6-orthoplex
1231:{3,3,3,3,4}
984:6-orthoplex
894:{3,3,3,3,3}
830:6-orthoplex
727:{4,3,3,3,3}
631:{3,3,3,3,4}
627:6-orthoplex
537:{3,3,3,3,3}
471:6-orthoplex
411:space group
70:(Hexeract)
50:6-orthoplex
2427:10-simplex
2411:9-demicube
2361:8-demicube
2311:7-demicube
2268:6-demicube
2238:5-demicube
2152:Octahedron
1787:References
1711:6-demicube
1074:6-demicube
851:diagram(s)
327:6-polytope
292:non-convex
230:hyperplane
219:5-polytope
215:polychoron
211:polyhedron
177:Definition
168:5-polytope
160:6-polytope
118:6-demicube
2475:orthoplex
2397:9-simplex
2347:8-simplex
2297:7-simplex
2254:6-simplex
2224:5-simplex
2193:Tesseract
1817:T. Gosset
1719:honeycomb
1589:(103680)
1237:{3,3,3,3}
994:{3,3,3,3}
844:symbol(s)
533:6-simplex
459:6-simplex
273:convexity
39:6-simplex
24:and five
20:of three
2550:Category
2529:Topics:
2492:demicube
2457:polytope
2451:Uniform
2212:600-cell
2208:120-cell
2161:Demicube
2135:Pentagon
2115:Triangle
1783:facets.
1705:are the
1472:polytope
1462:(51840)
1384:polytope
1068:(23040)
874:Symmetry
855:Vertices
842:Schläfli
811:(46080)
717:(46080)
521:Symmetry
502:Vertices
489:Schläfli
395:5-space
277:symmetry
183:vertices
164:polytope
152:geometry
2466:simplex
2436:10-cube
2203:24-cell
2189:16-cell
2130:Hexagon
1984:regular
1769:, has
1599:is the
1388:{3,3,3}
1369:(46080)
1212:(23040)
978:(1440)
870:5-faces
867:4-faces
849:Coxeter
517:5-faces
514:4-faces
498:diagram
496:Coxeter
384:squares
357:regular
275:" and "
207:polygon
22:regular
2406:9-cube
2356:8-cube
2306:7-cube
2263:6-cube
2233:5-cube
2120:Square
1997:Family
1873:
1703:facets
1645:. The
723:6-cube
621:(720)
491:symbol
465:6-cube
440:facets
386:and a
380:6-cube
347:has a
286:convex
171:facets
68:6-cube
18:Graphs
2125:p-gon
1476:{3,3}
1078:{3,3}
878:order
864:Cells
861:Faces
858:Edges
525:order
511:Cells
508:Faces
505:Edges
199:point
195:cells
191:faces
187:edges
162:is a
2483:cube
2156:Cube
1986:and
1871:ISBN
1709:and
1701:and
1595:The
1576:2160
1573:2160
1449:1080
1356:1200
1353:1120
838:Name
485:Name
444:cell
388:cube
248:and
154:, a
2032:(p)
1585:2×E
1579:702
1570:720
1527:or
1452:648
1446:720
1443:216
1371:2×D
1359:576
1350:480
1202:252
1199:640
1196:640
1193:240
1058:192
1055:240
1052:160
986:, 3
974:2×A
971:126
968:434
965:630
962:490
959:210
892:0,5
798:160
795:240
792:192
705:192
702:240
699:160
453::
279:".
158:or
147:In
2552::
2537:•
2533:•
2513:21
2509:•
2506:k1
2502:•
2499:k2
2477:•
2434:•
2404:•
2382:21
2378:•
2375:41
2371:•
2368:42
2354:•
2332:21
2328:•
2325:31
2321:•
2318:32
2304:•
2282:21
2278:•
2275:22
2261:•
2231:•
2210:•
2191:•
2170:•
2154:•
2086:/
2075:/
2065:/
2056:/
2034:/
1907::
1899:,
1892:,
1885:,
1843::
1833::
1823:,
1819::
1795:^
1780:21
1773:22
1717:22
1649:,
1607:,
1582:54
1567:72
1470:22
1455:99
1440:27
1382:21
1362:76
1347:60
1214:½B
1205:44
1190:32
1061:64
1049:60
1046:12
988:11
956:42
880:)
804:12
801:60
789:64
708:64
696:60
693:12
611:21
608:35
605:35
602:21
527:)
446:.
393:A
370:A
343:A
337:21
322:A
307:A
252:.
193:,
189:,
185:,
173:.
139:22
123:31
82:21
56:11
52:,
2521:-
2519:n
2511:k
2504:2
2497:1
2490:-
2488:n
2481:-
2479:n
2473:-
2471:n
2464:-
2462:n
2455:-
2453:n
2380:4
2373:2
2366:1
2330:3
2323:2
2316:1
2280:2
2273:1
2102:n
2100:H
2093:2
2090:G
2082:4
2079:F
2071:8
2068:E
2062:7
2059:E
2053:6
2050:E
2041:n
2037:D
2030:2
2027:I
2019:n
2015:B
2007:n
2003:A
1975:e
1968:t
1961:v
1919:.
1778:2
1771:1
1721:,
1715:2
1587:6
1468:1
1460:6
1458:E
1380:2
1373:6
1367:6
1365:B
1235:1
1233:t
1229:1
1227:t
1216:6
1210:6
1208:D
1066:6
1064:D
976:6
890:t
876:(
809:6
807:B
714:6
712:B
619:6
617:A
614:7
599:7
523:(
436:t
417:.
359:.
340:.
335:2
304:.
232:.
137:1
121:1
80:2
54:3
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
