24-cell honeycomb honeycomb
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!bgcolor=#e7dcc3 colspan=2|24-cell honeycomb honeycomb | |
| bgcolor=#ffffff align=center colspan=2|(No image) | |
| bgcolor=#e7dcc3|Type | Hyperbolic regular honeycomb |
| bgcolor=#e7dcc3|Schläfli symbol | {3,4,3,3,3} |
| bgcolor=#e7dcc3|Coxeter diagram | {{CDD|node_1|3|node|4|node|3|node|3|node|3|node}} {{CDD|node_1|branch3|splitsplit2|node|split1|nodes}} = {{CDD|node_1|3|node|4|node_g|3g|node_g|3sg|node_g|3g|node_g}} {{CDD|node_1|3|node|splitsplit1|branch3|3|node|4|node}} {{CDD|node_1|3|node|split1|nodes|4a4b|nodes}} |
| bgcolor=#e7dcc3|5-faces | 50px {3,4,3,3} |
| bgcolor=#e7dcc3|4-faces | 50px {3,4,3} |
| bgcolor=#e7dcc3|Cells | 50px {3,4} |
| bgcolor=#e7dcc3|Faces | 50px {3} |
| bgcolor=#e7dcc3|Cell figure | 50px {3} |
| bgcolor=#e7dcc3|Face figure | 50px {3,3} |
| bgcolor=#e7dcc3|Edge figure | 50px {3,3,3} |
| bgcolor=#e7dcc3|Vertex figure | 50px {4,3,3,3} |
| bgcolor=#e7dcc3|Dual | 5-orthoplex honeycomb |
| bgcolor=#e7dcc3|Coxeter group | {{overline|U}}5, [3,3,3,4,3] |
| bgcolor=#e7dcc3|Properties | Regular |
In the geometry of hyperbolic 5-space, the 24-cell honeycomb honeycomb is one of five paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite facets, whose vertices exist on 4-horospheres and converge to a single ideal point at infinity. With Schläfli symbol {3,4,3,3,3}, it has three 24-cell honeycombs around each cell. It is dual to the 5-orthoplex honeycomb.
Related honeycombs
It is related to the regular Euclidean 4-space 24-cell honeycomb, {3,4,3,3}, and the hyperbolic 5-space order-4 24-cell honeycomb honeycomb.
See also
References
- Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. {{ISBN|0-486-61480-8}}. (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
- Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 {{ISBN|0-486-40919-8}} (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II, III, IV, V, p212-213)