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 |