3453:
3123:
2833:
2625:
2347:
2128:
1917:
1702:
1413:
1115:
823:
568:
232:
2227:
2016:
1801:
1590:
3330:
3000:
2724:
2512:
483:
476:
3371:
3362:
3042:
3035:
1329:
1322:
1287:
1032:
1025:
990:
741:
706:
441:
109:
144:
1397:, {3,8}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many order-8 triangular tilings existing around each vertex in an
1099:, {3,8}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many order-8 triangular tilings existing around each vertex in an
808:, {3,8}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many order-8 triangular tilings existing around each vertex in an
553:, {3,8}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many order-8 triangular tilings existing around each vertex in an
3438:{â,8} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many order-8 apeirogonal tilings existing around each vertex in an
3108:, {6,8}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many hexagonal tilings existing around each vertex in an
217:{3,8} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many triangular tilings existing around each vertex in an
3511:
3660:
2818:
All vertices are ultra-ideal (existing beyond the ideal boundary) with five order-8 pentagonal tilings existing around each edge and with an
2260:
3656:
3498:
3314:
1496:
1271:
3584:
3564:
3542:
3488:
3304:
3158:
2979:
2491:
1486:
1261:
969:
603:
420:
3281:
2956:
2468:
1463:
1238:
946:
397:
3493:
3473:
3309:
3289:
3251:
3213:
3163:
3143:
2984:
2964:
2926:
2888:
2678:
2476:
2438:
2400:
2181:
1970:
1755:
1544:
1491:
1471:
1433:
1266:
1246:
1208:
1170:
974:
954:
916:
878:
660:
588:
405:
367:
329:
63:
3478:
3294:
3276:
3256:
3238:
3218:
2496:
2186:
1458:
1233:
1195:
608:
425:
3483:
3299:
3271:
3261:
3243:
3233:
3223:
3153:
2974:
2946:
2936:
2918:
2908:
2898:
2708:
2698:
2688:
2486:
2458:
2448:
2430:
2420:
2410:
2211:
2201:
2191:
2000:
1990:
1980:
1785:
1775:
1765:
1574:
1564:
1554:
1481:
1453:
1443:
1339:
1256:
1228:
1218:
1200:
1190:
1180:
964:
936:
926:
908:
898:
888:
690:
680:
670:
598:
415:
387:
377:
359:
349:
339:
93:
83:
73:
2048:
1833:
1622:
751:
3266:
3228:
3148:
2969:
2951:
2941:
2931:
2913:
2903:
2893:
2703:
2693:
2683:
2481:
2463:
2453:
2443:
2425:
2415:
2405:
2206:
2196:
1995:
1985:
1975:
1780:
1770:
1760:
1569:
1559:
1549:
1476:
1448:
1438:
1251:
1223:
1213:
1185:
1175:
959:
941:
931:
921:
903:
893:
883:
685:
675:
665:
593:
410:
392:
382:
372:
354:
344:
334:
88:
78:
68:
3679:
3574:
1042:
3646:
3439:
3365:
2267:
2055:
1840:
1629:
1500:, with alternating types or colors of order-8 triangular tiling cells. In Coxeter notation the half symmetry is = .
1317:
493:
3516:
3186:
2861:
2819:
2653:
2375:
2335:
The "ideal surface" projection below is a plane-at-infinity, in the
Poincaré half-space model of H3. It shows an
2156:
1945:
1883:
1796:
1730:
1519:
1394:
1282:
1143:
1096:
985:
851:
805:
701:
635:
550:
436:
304:
250:
214:
104:
38:
3435:
2310:
2222:
3533:
3109:
3105:
3030:
2611:
2542:
2098:
2011:
1020:
736:
554:
471:
2995:
2754:
3568:
3457:
3387:
3127:
3057:
2837:
2769:
2629:
2557:
2351:
2132:
1921:
1706:
1417:
1346:
1119:
1049:
827:
758:
572:
500:
236:
159:
3674:
3452:
3122:
2832:
2624:
2607:
2507:
2346:
2314:
2127:
2102:
1916:
1887:
1701:
1676:
1585:
1412:
1114:
822:
567:
231:
3427:
3097:
2808:
2596:
2306:
2094:
1879:
1668:
1386:
1088:
797:
539:
198:
3595:
3325:
3112:
557:
3466:
3431:
3193:
3136:
3101:
2868:
2812:
2660:
2600:
2382:
2321:
2163:
2109:
1952:
1894:
1737:
1683:
1526:
1426:
1390:
1150:
1092:
858:
801:
642:
581:
543:
311:
202:
45:
3642:
3580:
3560:
3552:
3538:
2336:
17:
3528:
3411:
3081:
2792:
2719:
2580:
2290:
2250:
2078:
2038:
1863:
1823:
1672:
1652:
1612:
1370:
1072:
781:
613:
523:
264:
218:
182:
139:
3167:, with alternating types or colors of cells. In Coxeter notation the half symmetry is = .
3205:
2880:
2670:
2392:
2173:
1962:
1747:
1536:
1162:
870:
652:
321:
253:
55:
3652:
3612:
267:
3668:
3442:
2822:
2614:
2329:
2245:
2117:
2033:
1906:
1818:
1691:
1607:
1402:
1104:
812:
221:
3423:
3093:
2804:
2592:
2302:
2090:
1875:
1664:
1382:
1084:
793:
535:
194:
3657:
Kleinian, a tool for visualizing
Kleinian groups, Geometry and the Imagination
3625:
3370:
3361:
3329:
3041:
3034:
2999:
2723:
2511:
2226:
2015:
1800:
1589:
1328:
1321:
1031:
1024:
740:
482:
475:
3634:
3350:
3340:
2606:
All vertices are ultra-ideal (existing beyond the ideal boundary) with four
2237:
2116:
is {6,8,3}, with three order-5 hexagonal tilings meeting at each edge. The
1307:
1690:
is {4,8,3}, with three order-4 octagonal tilings meeting at each edge. The
1286:
989:
705:
440:
108:
612:, with alternating types or colors of order-8 triangular tiling cells. In
3407:
3077:
2788:
2744:
2734:
2576:
2286:
2074:
1859:
1811:
1648:
1366:
1297:
1068:
1000:
777:
726:
716:
519:
451:
178:
129:
119:
143:
3628:
3545:. (Tables I and II: Regular polytopes and honeycombs, pp. 294â296)
3020:
3010:
2026:
1010:
2532:
2522:
1600:
461:
3556:
3608:
3604:
3174:
2849:
2641:
2363:
1131:
839:
623:
292:
26:
277:
It is a part of a sequence of self-dual regular honeycombs: {
2324:
of the apeirogonal tiling honeycomb is {â,8,3}, with three
2317:, each of which has a limiting circle on the ideal sphere.
2105:, each of which has a limiting circle on the ideal sphere.
1890:, each of which has a limiting circle on the ideal sphere.
1679:, each of which has a limiting circle on the ideal sphere.
3601:
Lorentzian
Coxeter groups and Boyd-Maxwell ball packings
2144:
1933:
1718:
1507:
263:
It is a part of a sequence of regular honeycombs with
249:
It is a part of a sequence of regular honeycombs with
3587:(Chapters 16â17: Geometries on Three-manifolds I, II)
3465:
It has a second construction as a uniform honeycomb,
3135:
It has a second construction as a uniform honeycomb,
1425:
It has a second construction as a uniform honeycomb,
580:
It has a second construction as a uniform honeycomb,
226:
3609:Visualizing Hyperbolic Honeycombs arXiv:1511.02851
3626:Hyperbolic Catacombs Carousel: {3,7,3} honeycomb
2332:of this honeycomb is an octagonal tiling, {8,3}.
2120:of this honeycomb is an octagonal tiling, {8,3}.
1909:of this honeycomb is an octagonal tiling, {8,3}.
1694:of this honeycomb is an octagonal tiling, {8,3}.
3592:Sphere Packings and Hyperbolic Reflection Groups
3512:Convex uniform honeycombs in hyperbolic space
3502:, with alternating types or colors of cells.
8:
2339:pattern of circles inside a largest circle.
3177:
2852:
2644:
2366:
2147:
1936:
1721:
1510:
1134:
842:
626:
295:
29:
3647:{7,3,3} Honeycomb Meets Plane at Infinity
3447:
3117:
2827:
2619:
2341:
2122:
1911:
1696:
1407:
1109:
817:
562:
3178:Order-8-infinite apeirogonal honeycomb
3569:Regular Honeycombs in Hyperbolic Space
3537:, 3rd. ed., Dover Publications, 1973.
3416:order-8-infinite apeirogonal honeycomb
3171:Order-8-infinite apeirogonal honeycomb
2610:existing around each edge and with an
1135:Order-8-infinite triangular honeycomb
3594:, JOURNAL OF ALGEBRA 79,78-97 (1982)
3549:The Beauty of Geometry: Twelve Essays
2309:). Each infinite cell consists of an
2097:). Each infinite cell consists of an
1882:). Each infinite cell consists of an
1671:). Each infinite cell consists of an
1375:order-8-infinite triangular honeycomb
1128:Order-8-infinite triangular honeycomb
7:
25:
3496:
3491:
3486:
3481:
3476:
3471:
3451:
3434:{â,8,â}. It has infinitely many
3369:
3360:
3328:
3312:
3307:
3302:
3297:
3292:
3287:
3279:
3274:
3269:
3264:
3259:
3254:
3249:
3241:
3236:
3231:
3226:
3221:
3216:
3211:
3161:
3156:
3151:
3146:
3141:
3121:
3040:
3033:
2998:
2982:
2977:
2972:
2967:
2962:
2954:
2949:
2944:
2939:
2934:
2929:
2924:
2916:
2911:
2906:
2901:
2896:
2891:
2886:
2831:
2722:
2706:
2701:
2696:
2691:
2686:
2681:
2676:
2623:
2510:
2494:
2489:
2484:
2479:
2474:
2466:
2461:
2456:
2451:
2446:
2441:
2436:
2428:
2423:
2418:
2413:
2408:
2403:
2398:
2345:
2225:
2209:
2204:
2199:
2194:
2189:
2184:
2179:
2148:Order-8-3 apeirogonal honeycomb
2126:
2014:
1998:
1993:
1988:
1983:
1978:
1973:
1968:
1915:
1799:
1783:
1778:
1773:
1768:
1763:
1758:
1753:
1700:
1588:
1572:
1567:
1562:
1557:
1552:
1547:
1542:
1494:
1489:
1484:
1479:
1474:
1469:
1461:
1456:
1451:
1446:
1441:
1436:
1431:
1411:
1393:{3,8,â}. It has infinitely many
1327:
1320:
1285:
1269:
1264:
1259:
1254:
1249:
1244:
1236:
1231:
1226:
1221:
1216:
1211:
1206:
1198:
1193:
1188:
1183:
1178:
1173:
1168:
1113:
1095:{3,8,6}. It has infinitely many
1030:
1023:
988:
972:
967:
962:
957:
952:
944:
939:
934:
929:
924:
919:
914:
906:
901:
896:
891:
886:
881:
876:
821:
739:
704:
688:
683:
678:
673:
668:
663:
658:
606:
601:
596:
591:
586:
566:
481:
474:
439:
423:
418:
413:
408:
403:
395:
390:
385:
380:
375:
370:
365:
357:
352:
347:
342:
337:
332:
327:
245:Related polytopes and honeycombs
230:
142:
107:
91:
86:
81:
76:
71:
66:
61:
3599:Hao Chen, Jean-Philippe Labbé,
3578:The Shape of Space, 2nd edition
3440:infinite-order octagonal tiling
3396:
3386:
3378:
3356:
3346:
3336:
3321:
3204:
3192:
3182:
3066:
3056:
3048:
3026:
3016:
3006:
2991:
2879:
2867:
2857:
2777:
2768:
2760:
2750:
2740:
2730:
2715:
2669:
2659:
2649:
2645:Order-8-5 pentagonal honeycomb
2565:
2556:
2548:
2538:
2528:
2518:
2503:
2391:
2381:
2371:
2295:order-8-3 apeirogonal honeycomb
2275:
2266:
2256:
2244:
2233:
2218:
2172:
2162:
2152:
2141:Order-8-3 apeirogonal honeycomb
2063:
2054:
2044:
2032:
2022:
2007:
1961:
1951:
1941:
1848:
1839:
1829:
1817:
1807:
1792:
1746:
1736:
1726:
1722:Order-8-3 pentagonal honeycomb
1637:
1628:
1618:
1606:
1596:
1581:
1535:
1525:
1515:
1399:infinite-order octagonal tiling
1355:
1345:
1335:
1313:
1303:
1293:
1278:
1161:
1149:
1139:
1057:
1048:
1038:
1016:
1006:
996:
981:
869:
857:
847:
843:Order-8-6 triangular honeycomb
766:
757:
747:
732:
722:
712:
697:
651:
641:
631:
627:Order-8-5 triangular honeycomb
508:
499:
489:
467:
457:
447:
432:
320:
310:
300:
296:Order-8-4 triangular honeycomb
167:
158:
150:
135:
125:
115:
100:
54:
44:
34:
30:Order-8-3 triangular honeycomb
3469:{â,(8,â,8)}, Coxeter diagram,
3139:{6,(8,3,8)}, Coxeter diagram,
2853:Order-8-6 hexagonal honeycomb
2797:order-8-5 pentagonal honeycomb
2638:Order-8-5 pentagonal honeycomb
1937:Order-8-3 hexagonal honeycomb
1899:order-6-3 pentagonal honeycomb
1868:order-8-3 pentagonal honeycomb
1715:Order-8-3 pentagonal honeycomb
1429:{3,(8,â,8)}, Coxeter diagram,
1077:order-8-6 triangular honeycomb
836:Order-8-6 triangular honeycomb
786:order-8-3 triangular honeycomb
620:Order-8-5 triangular honeycomb
528:order-8-4 triangular honeycomb
289:Order-8-4 triangular honeycomb
187:order-8-3 triangular honeycomb
1:
3422:) is a regular space-filling
3092:) is a regular space-filling
3086:order-8-6 hexagonal honeycomb
2846:Order-8-6 hexagonal honeycomb
2114:order-8-3 hexagonal honeycomb
2083:order-8-3 hexagonal honeycomb
1930:Order-8-3 hexagonal honeycomb
1381:) is a regular space-filling
1083:) is a regular space-filling
792:) is a regular space-filling
534:) is a regular space-filling
193:) is a regular space-filling
18:Order-8-6 hexagonal honeycomb
3551:(1999), Dover Publications,
2367:Order-8-4 square honeycomb
2328:meeting at each edge. The
2326:order-8 apeirogonal tilings
1511:Order-8-3 square honeycomb
3696:
3436:order-8 apeirogonal tiling
2803:) a regular space-filling
2591:) a regular space-filling
2585:order-8-4 square honeycomb
2360:Order-8-4 square honeycomb
2311:order-8 apeirogonal tiling
2301:) a regular space-filling
2089:) a regular space-filling
1905:meeting at each edge. The
1903:order-8 pentagonal tilings
1874:) a regular space-filling
1688:order-8-3 square honeycomb
1663:) a regular space-filling
1657:order-8-3 square honeycomb
1504:Order-8-3 square honeycomb
616:the half symmetry is = .
551:order-8 triangular tilings
3517:List of regular polytopes
3106:order-8 hexagonal tilings
2820:order-5 pentagonal tiling
1884:order-8 pentagonal tiling
1395:order-8 triangular tiling
1097:order-8 triangular tiling
806:order-8 triangular tiling
251:order-8 triangular tiling
215:order-8 triangular tiling
3110:order-6 octagonal tiling
2612:order-4 octagonal tiling
2313:whose vertices lie on a
2101:whose vertices lie on a
2099:order-6 hexagonal tiling
1886:whose vertices lie on a
1675:whose vertices lie on a
1101:order-6 octagonal tiling
810:order-5 octagonal tiling
584:{3,8}, Coxeter diagram,
555:order-4 hexagonal tiling
1901:is {5,8,3}, with three
2608:order-5 square tilings
804:{3,8,5}. It has five
3680:Regular 3-honeycombs
3104:{6,8,6}. It has six
3458:Poincaré disk model
3128:Poincaré disk model
2838:Poincaré disk model
2630:Poincaré disk model
2352:Poincaré disk model
2133:Poincaré disk model
1922:Poincaré disk model
1707:Poincaré disk model
1418:Poincaré disk model
1120:Poincaré disk model
828:Poincaré disk model
573:Poincaré disk model
237:Poincaré disk model
3412:hyperbolic 3-space
3113:vertex arrangement
3082:hyperbolic 3-space
2793:hyperbolic 3-space
2581:hyperbolic 3-space
2291:hyperbolic 3-space
2079:hyperbolic 3-space
1864:hyperbolic 3-space
1653:hyperbolic 3-space
1371:hyperbolic 3-space
1073:hyperbolic 3-space
782:hyperbolic 3-space
558:vertex arrangement
524:hyperbolic 3-space
183:hyperbolic 3-space
3643:{7,3,3} Honeycomb
3534:Regular Polytopes
3463:
3462:
3404:
3403:
3187:Regular honeycomb
3133:
3132:
3074:
3073:
2862:Regular honeycomb
2843:
2842:
2785:
2784:
2654:Regular honeycomb
2635:
2634:
2573:
2572:
2376:Regular honeycomb
2357:
2356:
2337:Apollonian gasket
2283:
2282:
2157:Regular honeycomb
2138:
2137:
2071:
2070:
1946:Regular honeycomb
1927:
1926:
1856:
1855:
1731:Regular honeycomb
1712:
1711:
1645:
1644:
1520:Regular honeycomb
1423:
1422:
1363:
1362:
1144:Regular honeycomb
1125:
1124:
1065:
1064:
852:Regular honeycomb
833:
832:
774:
773:
636:Regular honeycomb
578:
577:
516:
515:
305:Regular honeycomb
242:
241:
175:
174:
39:Regular honeycomb
16:(Redirected from
3687:
3590:George Maxwell,
3575:Jeffrey R. Weeks
3501:
3500:
3499:
3495:
3494:
3490:
3489:
3485:
3484:
3480:
3479:
3475:
3474:
3455:
3448:
3373:
3364:
3332:
3317:
3316:
3315:
3311:
3310:
3306:
3305:
3301:
3300:
3296:
3295:
3291:
3290:
3284:
3283:
3282:
3278:
3277:
3273:
3272:
3268:
3267:
3263:
3262:
3258:
3257:
3253:
3252:
3246:
3245:
3244:
3240:
3239:
3235:
3234:
3230:
3229:
3225:
3224:
3220:
3219:
3215:
3214:
3206:Coxeter diagrams
3194:SchlÀfli symbols
3175:
3166:
3165:
3164:
3160:
3159:
3155:
3154:
3150:
3149:
3145:
3144:
3125:
3118:
3044:
3037:
3002:
2987:
2986:
2985:
2981:
2980:
2976:
2975:
2971:
2970:
2966:
2965:
2959:
2958:
2957:
2953:
2952:
2948:
2947:
2943:
2942:
2938:
2937:
2933:
2932:
2928:
2927:
2921:
2920:
2919:
2915:
2914:
2910:
2909:
2905:
2904:
2900:
2899:
2895:
2894:
2890:
2889:
2881:Coxeter diagrams
2869:SchlÀfli symbols
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1673:octagonal tiling
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46:SchlÀfli symbols
27:
21:
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3639:Visual insights
3622:
3525:
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3497:
3492:
3487:
3482:
3477:
3472:
3470:
3467:SchlÀfli symbol
3456:
3432:SchlÀfli symbol
3420:â,8,â honeycomb
3392:
3368:
3313:
3308:
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3298:
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3137:SchlÀfli symbol
3126:
3102:SchlÀfli symbol
3090:6,8,6 honeycomb
3062:
3038:
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2813:SchlÀfli symbol
2801:5,8,5 honeycomb
2707:
2702:
2697:
2692:
2687:
2682:
2677:
2675:
2661:SchlÀfli symbol
2640:
2628:
2601:SchlÀfli symbol
2589:4,8,4 honeycomb
2495:
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2383:SchlÀfli symbol
2362:
2350:
2322:SchlÀfli symbol
2299:â,8,3 honeycomb
2210:
2205:
2200:
2195:
2190:
2185:
2180:
2178:
2174:Coxeter diagram
2164:SchlÀfli symbol
2143:
2131:
2110:SchlÀfli symbol
2087:6,8,3 honeycomb
1999:
1994:
1989:
1984:
1979:
1974:
1969:
1967:
1963:Coxeter diagram
1953:SchlÀfli symbol
1932:
1920:
1895:SchlÀfli symbol
1872:5,8,3 honeycomb
1784:
1779:
1774:
1769:
1764:
1759:
1754:
1752:
1748:Coxeter diagram
1738:SchlÀfli symbol
1717:
1705:
1684:SchlÀfli symbol
1661:4,8,3 honeycomb
1573:
1568:
1563:
1558:
1553:
1548:
1543:
1541:
1537:Coxeter diagram
1527:SchlÀfli symbol
1506:
1495:
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1468:
1462:
1457:
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1427:SchlÀfli symbol
1416:
1391:SchlÀfli symbol
1379:3,8,â honeycomb
1351:
1325:
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1093:SchlÀfli symbol
1081:3,8,6 honeycomb
1028:
973:
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826:
802:SchlÀfli symbol
790:3,8,5 honeycomb
689:
684:
679:
674:
669:
664:
659:
657:
622:
607:
602:
597:
592:
587:
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582:SchlÀfli symbol
571:
544:SchlÀfli symbol
532:3,8,4 honeycomb
479:
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396:
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203:SchlÀfli symbol
191:3,8,3 honeycomb
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62:
60:
23:
22:
15:
12:
11:
5:
3693:
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3683:
3682:
3677:
3667:
3666:
3663:
3662:
3659:4 March 2014.
3653:Danny Calegari
3650:
3632:
3631:, Roice Nelson
3621:
3620:External links
3618:
3617:
3616:
3613:Henry Segerman
3611:Roice Nelson,
3606:
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3645:(2014/08/01)
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3585:0-8247-0709-5
3582:
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3573:
3570:
3567:(Chapter 10,
3566:
3565:0-486-40919-8
3562:
3558:
3554:
3550:
3547:
3544:
3543:0-486-61480-8
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3388:Coxeter group
3385:
3381:
3377:
3372:
3367:
3363:
3359:
3357:Vertex figure
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3058:Coxeter group
3055:
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3047:
3043:
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3027:Vertex figure
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2770:Coxeter group
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2763:
2759:
2756:
2753:
2751:Vertex figure
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2268:Coxeter group
2265:
2262:
2259:
2255:
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2249:
2247:
2246:Vertex figure
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2056:Coxeter group
2053:
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2034:Vertex figure
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2013:
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1966:
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1869:
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1841:Coxeter group
1838:
1835:
1832:
1828:
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1819:Vertex figure
1816:
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1749:
1745:
1741:
1739:
1735:
1732:
1729:
1725:
1720:
1714:
1708:
1703:
1699:
1698:
1695:
1693:
1692:vertex figure
1689:
1685:
1680:
1678:
1674:
1670:
1666:
1662:
1658:
1654:
1650:
1640:
1636:
1633:
1631:
1630:Coxeter group
1627:
1624:
1621:
1617:
1614:
1611:
1609:
1608:Vertex figure
1605:
1602:
1599:
1595:
1591:
1587:
1584:
1580:
1540:
1538:
1534:
1530:
1528:
1524:
1521:
1518:
1514:
1509:
1503:
1501:
1428:
1419:
1414:
1410:
1409:
1406:
1404:
1403:vertex figure
1400:
1396:
1392:
1388:
1384:
1380:
1376:
1372:
1368:
1358:
1354:
1350:
1348:
1347:Coxeter group
1344:
1341:
1338:
1334:
1330:
1323:
1319:
1316:
1314:Vertex figure
1312:
1309:
1306:
1302:
1299:
1296:
1292:
1288:
1284:
1281:
1277:
1166:
1164:
1160:
1154:
1152:
1148:
1145:
1142:
1138:
1133:
1127:
1121:
1116:
1112:
1111:
1108:
1106:
1105:vertex figure
1102:
1098:
1094:
1090:
1086:
1082:
1078:
1074:
1070:
1060:
1056:
1053:
1051:
1050:Coxeter group
1047:
1044:
1041:
1037:
1033:
1026:
1022:
1019:
1017:Vertex figure
1015:
1012:
1009:
1005:
1002:
999:
995:
991:
987:
984:
980:
874:
872:
868:
862:
860:
856:
853:
850:
846:
841:
835:
829:
824:
820:
819:
816:
814:
813:vertex figure
811:
807:
803:
799:
795:
791:
787:
783:
779:
769:
765:
762:
760:
759:Coxeter group
756:
753:
750:
746:
742:
738:
735:
733:Vertex figure
731:
728:
725:
721:
718:
715:
711:
707:
703:
700:
696:
656:
654:
650:
646:
644:
640:
637:
634:
630:
625:
619:
617:
615:
583:
574:
569:
565:
564:
561:
559:
556:
552:
547:
545:
541:
537:
533:
529:
525:
521:
511:
507:
504:
502:
501:Coxeter group
498:
495:
492:
488:
484:
477:
473:
470:
468:Vertex figure
466:
463:
460:
456:
453:
450:
446:
442:
438:
435:
431:
325:
323:
319:
315:
313:
309:
306:
303:
299:
294:
288:
286:
284:
280:
275:
273:
269:
266:
261:
259:
255:
252:
244:
238:
233:
229:
228:
225:
223:
222:vertex figure
220:
216:
213:It has three
208:
206:
204:
200:
196:
192:
188:
184:
180:
170:
166:
163:
161:
160:Coxeter group
157:
153:
149:
145:
141:
138:
136:Vertex figure
134:
131:
128:
124:
121:
118:
114:
110:
106:
103:
99:
59:
57:
53:
49:
47:
43:
40:
37:
33:
28:
19:
3675:3-honeycombs
3649:(2014/08/14)
3638:
3600:
3591:
3577:
3548:
3532:
3464:
3424:tessellation
3419:
3415:
3405:
3200:{â,(8,â,8)}
3134:
3094:tessellation
3089:
3085:
3075:
2875:{6,(8,3,8)}
2817:
2805:tessellation
2800:
2796:
2786:
2605:
2593:tessellation
2588:
2584:
2574:
2334:
2325:
2319:
2315:2-hypercycle
2303:tessellation
2298:
2294:
2284:
2113:
2107:
2103:2-hypercycle
2091:tessellation
2086:
2082:
2072:
1902:
1898:
1892:
1888:2-hypercycle
1876:tessellation
1871:
1867:
1857:
1687:
1681:
1677:2-hypercycle
1665:tessellation
1660:
1656:
1646:
1424:
1398:
1383:tessellation
1378:
1374:
1364:
1157:{3,(8,â,8)}
1100:
1085:tessellation
1080:
1076:
1066:
865:{3,(8,3,8)}
809:
794:tessellation
789:
785:
775:
579:
549:It has four
548:
536:tessellation
531:
527:
517:
282:
278:
276:
271:
262:
257:
248:
212:
195:tessellation
190:
186:
176:
3571:) Table III
3347:Edge figure
3017:Edge figure
2741:Edge figure
2529:Edge figure
1304:Edge figure
1007:Edge figure
723:Edge figure
458:Edge figure
126:Edge figure
3669:Categories
3523:References
3397:Properties
3382:self-dual
3374:{(8,â,8)}
3067:Properties
3052:self-dual
3039:{(5,3,5)}
2778:Properties
2764:self-dual
2566:Properties
2552:self-dual
2276:Properties
2064:Properties
1849:Properties
1638:Properties
1356:Properties
1326:{(8,â,8)}
1058:Properties
1029:{(8,3,8)}
767:Properties
509:Properties
168:Properties
154:Self-dual
3635:John Baez
3428:honeycomb
3098:honeycomb
2815:{5,8,5}.
2809:honeycomb
2603:{4,8,4}.
2597:honeycomb
2307:honeycomb
2238:Apeirogon
2095:honeycomb
1880:honeycomb
1669:honeycomb
1401:, {8,â},
1387:honeycomb
1103:, {8,6},
1089:honeycomb
798:honeycomb
546:{3,8,4}.
540:honeycomb
205:{3,8,3}.
199:honeycomb
3603:, (2013)
3557:99-35678
3506:See also
3408:geometry
3400:Regular
3078:geometry
3070:Regular
2789:geometry
2781:Regular
2665:{5,8,5}
2577:geometry
2569:Regular
2387:{4,8,4}
2287:geometry
2279:Regular
2168:{â,8,3}
2075:geometry
2067:Regular
1957:{6,8,3}
1860:geometry
1852:Regular
1742:{5,8,3}
1649:geometry
1641:Regular
1531:{4,8,3}
1367:geometry
1359:Regular
1069:geometry
1061:Regular
778:geometry
770:Regular
647:{3,8,5}
520:geometry
512:Regular
316:{3,8,4}
209:Geometry
179:geometry
171:Regular
50:{3,8,3}
3629:YouTube
3529:Coxeter
3430:) with
3406:In the
3198:{â,8,â}
3100:) with
3076:In the
2873:{6,8,6}
2811:) with
2787:In the
2599:) with
2575:In the
2285:In the
2261:{3,8,â}
2112:of the
2073:In the
2049:{3,8,6}
1897:of the
1858:In the
1834:{3,8,5}
1686:of the
1647:In the
1623:{3,8,4}
1389:) with
1365:In the
1340:{â,8,3}
1155:{3,8,â}
1091:) with
1067:In the
1043:{6,8,3}
863:{3,8,6}
800:) with
776:In the
752:{5,8,3}
542:) with
518:In the
494:{4,8,3}
480:r{8,8}
274:,8,3}.
256:: {3,8,
201:) with
177:In the
3615:(2015)
3583:
3563:
3555:
3541:
3414:, the
3084:, the
2795:, the
2583:, the
2293:, the
2081:, the
1866:, the
1655:, the
1373:, the
1075:, the
784:, the
526:, the
185:, the
3366:{8,â}
3337:Faces
3326:{â,8}
3322:Cells
3031:{8,6}
3007:Faces
2996:{6,8}
2992:Cells
2755:{8,5}
2731:Faces
2720:{5,8}
2716:Cells
2543:{8,4}
2519:Faces
2508:{4,8}
2504:Cells
2251:{8,3}
2234:Faces
2223:{â,8}
2219:Cells
2039:{8,3}
2023:Faces
2012:{6,8}
2008:Cells
1824:{8,3}
1808:Faces
1797:{5,8}
1793:Cells
1613:{8,3}
1597:Faces
1586:{4,8}
1582:Cells
1318:{8,â}
1294:Faces
1283:{3,8}
1279:Cells
1021:{8,6}
997:Faces
986:{3,8}
982:Cells
737:{8,5}
713:Faces
702:{3,8}
698:Cells
472:{8,4}
448:Faces
437:{3,8}
433:Cells
254:cells
140:{8,3}
116:Faces
105:{3,8}
101:Cells
3581:ISBN
3561:ISBN
3553:LCCN
3539:ISBN
3426:(or
3418:(or
3379:Dual
3183:Type
3096:(or
3088:(or
3049:Dual
2858:Type
2807:(or
2799:(or
2761:Dual
2650:Type
2595:(or
2587:(or
2549:Dual
2372:Type
2320:The
2305:(or
2297:(or
2257:Dual
2240:{â}
2153:Type
2108:The
2093:(or
2085:(or
2045:Dual
1942:Type
1893:The
1878:(or
1870:(or
1830:Dual
1727:Type
1682:The
1667:(or
1659:(or
1619:Dual
1516:Type
1385:(or
1377:(or
1336:Dual
1140:Type
1087:(or
1079:(or
1039:Dual
848:Type
796:(or
788:(or
748:Dual
632:Type
538:(or
530:(or
490:Dual
301:Type
197:(or
189:(or
151:Dual
35:Type
3410:of
3351:{â}
3341:{â}
3080:of
3021:{6}
3011:{6}
2791:of
2745:{5}
2735:{5}
2579:of
2533:{4}
2523:{4}
2289:of
2077:of
2027:{6}
1862:of
1812:{5}
1651:of
1601:{4}
1369:of
1308:{â}
1298:{3}
1071:of
1011:{6}
1001:{3}
780:of
727:{5}
717:{3}
522:of
462:{4}
452:{3}
285:}.
281:,8,
270:: {
260:}.
181:of
130:{3}
120:{3}
3671::
3655:,
3641::
3637:,
3559:,
3531:,
3445:.
3285:â
3115:.
2960:=
2825:.
2617:.
2472:=
1467:=
1405:.
1242:=
1107:.
950:=
815:.
560:.
401:=
224:.
283:p
279:p
272:p
258:p
20:)
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