Order-5 tesseractic honeycomb
| Order-5 tesseractic honeycomb | |
|---|---|
| (No image) | |
| Type | Hyperbolic regular honeycomb |
| Schläfli symbol | {4,3,3,5} |
| Coxeter diagram |     
|
| 4-faces |  {4,3,3}
|
| Cells |  {4,3}
|
| Faces |  {4}
|
| Face figure |  {5}
|
| Edge figure |  {3,5}
|
| Vertex figure |  {3,3,5}
|
| Dual | Order-4 120-cell honeycomb |
| Coxeter group | BH4, [5,3,3,4] |
| Properties | Regular |
In the geometry of hyperbolic 4-space, the order-5 tesseractic honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {4,3,3,5}, it has five 8-cells (also known as tesseracts) around each face. Its dual is the order-4 120-cell honeycomb, {5,3,3,4}.
Related polytopes and honeycombs
[edit]It is related to the Euclidean 4-space (order-4) tesseractic honeycomb, {4,3,3,4}, and the 5-cube, {4,3,3,3} in Euclidean 5-space. The 5-cube can also be seen as an order-3 tesseractic honeycomb on the surface of a 4-sphere.
See also
[edit]References
[edit]- 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)