1900:
1550:
227:
1226:
1219:
1212:
788:
781:
774:
1254:
1247:
1240:
1233:
760:
753:
1912:
1562:
239:
746:
994:
144:
1779:
1429:
109:
937:
1471:
767:
1095:
1033:
898:
1821:
1814:
1464:
841:
802:
2009:
1885:{3,3} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many tetrahedra existing around each vertex in an
1535:{3,3} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many tetrahedra existing around each vertex in an
207:{3,3} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many tetrahedra existing around each vertex in an
2149:
663:
2145:
1996:
1763:
1149:
733:
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2062:
2040:
1963:
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1380:
1991:
1986:
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479:
436:
418:
403:
365:
322:
63:
1958:
1725:
1687:
1121:
890:
695:
423:
1981:
1953:
1943:
1748:
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332:
93:
83:
73:
1193:
1183:
1976:
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1743:
1715:
1705:
1677:
1667:
1588:
1393:
1375:
1365:
1355:
1337:
1327:
1317:
1111:
1059:
1049:
1020:
1010:
963:
953:
924:
914:
867:
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828:
818:
713:
685:
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636:
618:
608:
598:
575:
565:
555:
522:
504:
494:
484:
461:
451:
441:
408:
390:
380:
370:
347:
337:
327:
88:
78:
68:
2163:
2072:
1188:
586:
472:
1917:
1831:
1567:
244:
2135:
154:
1203:
1481:
1198:
2014:
1635:
1536:
1459:
1285:
1159:
1037:
998:
208:
139:
38:
2031:
1899:
1549:
1225:
1218:
1211:
1178:
787:
780:
773:
226:
2066:
1904:
1838:
1554:
1488:
231:
161:
1253:
1246:
1239:
1232:
2000:, with alternating types or colors of tetrahedral cells. In Coxeter notation the half symmetry is = .
1874:
1524:
196:
2093:
2168:
759:
1889:
1539:
211:
1926:
1878:
1642:
1576:
1528:
1292:
752:
200:
45:
2131:
1911:
1561:
745:
238:
2078:
2058:
2050:
2036:
941:
258:
17:
2026:
1862:
1613:
1512:
291:
184:
993:
143:
1778:
1654:
1428:
1304:
265:
108:
55:
2141:
2110:
1470:
2157:
1162:
936:
1870:
1520:
192:
1774:
1424:
902:
806:
262:
104:
766:
2146:
Kleinian, a tool for visualizing
Kleinian groups, Geometry and the Imagination
1882:
1820:
1813:
1532:
1094:
845:
204:
2123:
1799:
1463:
1032:
897:
840:
1858:
1789:
1508:
1439:
429:
286:
180:
129:
119:
801:
2043:. (Tables I and II: Regular polytopes and honeycombs, pp. 294â296)
1449:
358:
315:
2054:
2106:
2102:
1623:
1273:
26:
1612:, with alternating types or colors of tetrahedral cells. In
1916:
Rendered intersection of honeycomb with the ideal plane in
1566:
Rendered intersection of honeycomb with the ideal plane in
243:
Rendered intersection of honeycomb with the ideal plane in
1158:
It is a part of a sequence of hyperbolic honeycombs with
2099:
Lorentzian
Coxeter groups and Boyd-Maxwell ball packings
1262:
It is a part of a sequence of hyperbolic honeycombs, {3,
2085:(Chapters 16â17: Geometries on Three-manifolds I, II)
1925:
It has a second construction as a uniform honeycomb,
1575:
It has a second construction as a uniform honeycomb,
1894:
1544:
221:
2107:Visualizing Hyperbolic Honeycombs arXiv:1511.02851
2090:Sphere Packings and Hyperbolic Reflection Groups
2010:Convex uniform honeycombs in hyperbolic space
8:
1626:
1276:
29:
274:
2136:{7,3,3} Honeycomb Meets Plane at Infinity
1171:
2067:Regular Honeycombs in Hyperbolic Space
2035:, 3rd. ed., Dover Publications, 1973.
2092:, JOURNAL OF ALGEBRA 79,78-97 (1982)
2047:The Beauty of Geometry: Twelve Essays
1627:Infinite-order tetrahedral honeycomb
7:
1867:infinite-order tetrahedral honeycomb
1620:Infinite-order tetrahedral honeycomb
25:
1994:
1989:
1984:
1979:
1974:
1969:
1961:
1956:
1951:
1946:
1941:
1936:
1931:
1910:
1898:
1887:infinite-order triangular tiling
1881:{3,3,â}. It has infinitely many
1819:
1812:
1777:
1761:
1756:
1751:
1746:
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1718:
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621:
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578:
573:
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558:
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507:
502:
497:
492:
487:
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477:
464:
459:
454:
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444:
439:
434:
421:
416:
411:
406:
401:
393:
388:
383:
378:
373:
368:
363:
350:
345:
340:
335:
330:
325:
320:
253:Related polytopes and honeycombs
237:
225:
142:
107:
91:
86:
81:
76:
71:
66:
61:
2097:Hao Chen, Jean-Philippe Labbé,
2076:The Shape of Space, 2nd edition
1847:
1837:
1827:
1805:
1795:
1785:
1770:
1653:
1641:
1631:
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1420:
1303:
1291:
1281:
169:
160:
150:
135:
125:
115:
100:
54:
44:
34:
1929:{3,(3,â,3)}, Coxeter diagram,
1579:{3,(3,4,3)}, Coxeter diagram,
1277:Order-8 tetrahedral honeycomb
257:It is a part of a sequence of
30:Order-7 tetrahedral honeycomb
1:
1517:order-8 tetrahedral honeycomb
1270:Order-8 tetrahedral honeycomb
189:order-7 tetrahedral honeycomb
18:Order-8 tetrahedral honeycomb
2049:(1999), Dover Publications,
1636:Hyperbolic regular honeycomb
1286:Hyperbolic regular honeycomb
39:Hyperbolic regular honeycomb
1869:is a regular space-filling
1519:is a regular space-filling
191:is a regular space-filling
2185:
1616:the half symmetry is = .
277:
2015:List of regular polytopes
1918:Poincaré half-space model
1568:Poincaré half-space model
1537:order-8 triangular tiling
1160:order-7 triangular tiling
306:
300:
290:
285:
245:Poincaré half-space model
209:order-7 triangular tiling
1531:{3,3,8}. It has eight
203:{3,3,7}. It has seven
2164:Regular 3-honeycombs
261:and honeycombs with
1905:Poincaré disk model
1555:Poincaré disk model
232:Poincaré disk model
1890:vertex arrangement
1863:hyperbolic 3-space
1540:vertex arrangement
1513:hyperbolic 3-space
278:{3,3,p} polytopes
212:vertex arrangement
185:hyperbolic 3-space
2132:{7,3,3} Honeycomb
2032:Regular Polytopes
1923:
1922:
1855:
1854:
1573:
1572:
1505:
1504:
1260:
1259:
1156:
1155:
259:regular polychora
250:
249:
177:
176:
16:(Redirected from
2176:
2088:George Maxwell,
2073:Jeffrey R. Weeks
1999:
1998:
1997:
1993:
1992:
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1987:
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1982:
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1907:(cell-centered)
1902:
1895:
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1669:
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1663:
1655:Coxeter diagrams
1643:SchlÀfli symbols
1624:
1614:Coxeter notation
1611:
1610:
1609:
1605:
1604:
1600:
1599:
1595:
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1557:(cell-centered)
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1305:Coxeter diagrams
1293:SchlÀfli symbols
1274:
1256:
1249:
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1214:
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234:(cell-centered)
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146:
111:
96:
95:
94:
90:
89:
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56:Coxeter diagrams
46:SchlÀfli symbols
27:
21:
2184:
2183:
2179:
2178:
2177:
2175:
2174:
2173:
2154:
2153:
2128:Visual insights
2120:
2023:
2006:
1995:
1990:
1985:
1980:
1975:
1970:
1968:
1962:
1957:
1952:
1947:
1942:
1937:
1932:
1930:
1927:SchlÀfli symbol
1915:
1903:
1879:SchlÀfli symbol
1843:
1817:
1762:
1757:
1752:
1747:
1742:
1737:
1735:
1729:
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1602:
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1582:
1580:
1577:SchlÀfli symbol
1565:
1553:
1529:SchlÀfli symbol
1493:
1467:
1412:
1407:
1402:
1397:
1392:
1387:
1385:
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201:SchlÀfli symbol
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5:
2182:
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2156:
2155:
2152:
2151:
2148:4 March 2014.
2142:Danny Calegari
2139:
2119:
2118:External links
2116:
2115:
2114:
2111:Henry Segerman
2109:Roice Nelson,
2104:
2095:
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2019:
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1176:
1163:vertex figures
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2134:(2014/08/01)
2133:
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2083:0-8247-0709-5
2080:
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2065:(Chapter 10,
2064:
2063:0-486-40919-8
2060:
2056:
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2048:
2045:
2042:
2041:0-486-61480-8
2038:
2034:
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2028:
2025:
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2020:
2016:
2013:
2011:
2008:
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2001:
1928:
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1864:
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1846:
1842:
1840:
1839:Coxeter group
1836:
1833:
1830:
1826:
1822:
1815:
1811:
1808:
1806:Vertex figure
1804:
1801:
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1456:Vertex figure
1454:
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771:
768:
764:
761:
757:
754:
750:
747:
743:
740:
739:
665:
664:{3,3,∞}
661:
588:
585:
545:
542:
474:
471:
431:
428:
360:
357:
317:
314:
311:
310:
303:
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172:
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162:Coxeter group
159:
156:
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149:
145:
141:
138:
136:Vertex figure
134:
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128:
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118:
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103:
99:
59:
57:
53:
49:
47:
43:
40:
37:
33:
28:
19:
2138:(2014/08/14)
2127:
2098:
2089:
2075:
2046:
2030:
1924:
1871:tessellation
1866:
1856:
1649:{3,(3,â,3)}
1574:
1521:tessellation
1516:
1506:
1299:{3,(3,4,3)}
1263:
1261:
1166:
1157:
543:
304:Paracompact
269:
256:
193:tessellation
188:
178:
2069:) Table III
1796:Edge figure
1446:Edge figure
1100:{3,∞}
307:Noncompact
263:tetrahedral
126:Edge figure
2169:Tetrahedra
2158:Categories
2021:References
1883:tetrahedra
1848:Properties
1818:{(3,â,3)}
1533:tetrahedra
1498:Properties
1468:{(3,4,3)}
205:tetrahedra
170:Properties
2124:John Baez
1875:honeycomb
1525:honeycomb
197:honeycomb
2101:, (2013)
2055:99-35678
2004:See also
1859:geometry
1851:Regular
1509:geometry
1501:Regular
1175:{3,3,7}
181:geometry
173:Regular
50:{3,3,7}
2027:Coxeter
1877:) with
1857:In the
1832:{â,3,3}
1647:{3,3,â}
1527:) with
1507:In the
1482:{8,3,3}
1297:{3,3,8}
1204:{â,3,7}
1199:{8,3,7}
1194:{7,3,7}
1189:{6,3,7}
1184:{5,3,7}
1179:{4,3,7}
1169:,3,7}.
797:figure
587:{3,3,8}
544:{3,3,7}
473:{3,3,6}
430:{3,3,5}
359:{3,3,4}
316:{3,3,3}
301:Finite
268:, {3,3,
199:) with
179:In the
155:{7,3,3}
2113:(2015)
2081:
2061:
2053:
2039:
1865:, the
1515:, the
795:Vertex
741:Image
283:Space
218:Images
187:, the
1810:{3,â}
1786:Faces
1775:{3,3}
1771:Cells
1460:{3,8}
1436:Faces
1425:{3,3}
1421:Cells
1266:,7}.
1038:{3,8}
999:{3,7}
942:{3,6}
903:{3,5}
846:{3,4}
807:{3,3}
312:Name
298:Form
266:cells
140:{3,7}
116:Faces
105:{3,3}
101:Cells
2079:ISBN
2059:ISBN
2051:LCCN
2037:ISBN
1873:(or
1828:Dual
1632:Type
1523:(or
1478:Dual
1282:Type
662:...
195:(or
151:Dual
35:Type
1861:of
1800:{â}
1790:{3}
1511:of
1450:{8}
1440:{3}
1165:, {
272:}.
183:of
130:{7}
120:{3}
2160::
2144:,
2130::
2126:,
2057:,
2029:,
1967:=
1892:.
1734:=
1542:.
1384:=
214:.
1264:p
1167:p
292:H
287:S
270:p
20:)
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