24-cell honeycomb honeycomb
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.
| 24-cell honeycomb honeycomb | |
|---|---|
| (No image) | |
| Type | Hyperbolic regular honeycomb |
| Schläfli symbol | {3,4,3,3,3} |
| Coxeter diagram |         =      |
| 5-faces |  {3,4,3,3} |
| 4-faces |  {3,4,3} |
| Cells |  {3,4} |
| Faces |  {3} |
| Cell figure | {3} |
| Face figure |  {3,3} |
| Edge figure |  {3,3,3} |
| Vertex figure |  {4,3,3,3} |
| Dual | 5-orthoplex honeycomb |
| Coxeter group | U5, [3,3,3,4,3] |
| Properties | Regular |
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)
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