Order-4 24-cell honeycomb
| Order-4 24-cell honeycomb | |
|---|---|
| (No image) | |
| Type | Hyperbolic regular honeycomb |
| Schläfli symbol | {3,4,3,4} {3,4,31,1} |
| Coxeter diagram |       ↔ 
|
| 4-faces |  {3,4,3}
|
| Cells |  {3,4}
|
| Faces |  {3}
|
| Face figure |  {4}
|
| Edge figure | {3,4}
|
| Vertex figure |  {4,3,4}
|
| Dual | Cubic honeycomb honeycomb |
| Coxeter group | R4, [4,3,4,3] |
| Properties | Regular |
In the geometry of hyperbolic 4-space, the order-4 24-cell honeycomb is one of two paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite vertex figures, with all vertices as ideal points at infinity. With Schläfli symbol {3,4,3,4}, it has four 24-cells around each face. It is dual to the cubic honeycomb honeycomb.
Related honeycombs
[edit]It is related to the regular Euclidean 4-space 24-cell honeycomb, {3,4,3,3}, with 24-cell facets.
See also
[edit]References
[edit]- 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)