Cubic honeycomb honeycomb
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| Cubic honeycomb honeycomb | |
|---|---|
| (No image) | |
| Type | Hyperbolic regular honeycomb |
| Schläfli symbol | {4,3,4,3} {4,31,1,1} |
| Coxeter diagram |       ↔         ↔ |
| 4-faces |  {4,3,4} |
| Cells |  {4,3} |
| Faces |  {4} |
| Face figure |  {3} |
| Edge figure | {4,3} |
| Vertex figure |  {3,4,3} |
| Dual | Order-4 24-cell honeycomb |
| Coxeter group | R4, [4,3,4,3] |
| Properties | Regular |
In the geometry of hyperbolic 4-space, the cubic honeycomb honeycomb is one of two paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite facets, whose vertices exist on 3-horospheres and converge to a single ideal point at infinity. With Schläfli symbol {4,3,4,3}, it has three cubic honeycombs around each face, and with a {3,4,3} vertex figure. It is dual to the order-4 24-cell honeycomb.