Order-5 120-cell honeycomb
| Order-5 120-cell honeycomb | |
|---|---|
| (No image) | |
| Type | Hyperbolic regular honeycomb |
| Schläfli symbol | {5,3,3,5} |
| Coxeter diagram |    
|
| 4-faces |  {5,3,3}
|
| Cells |  {5,3}
|
| Faces |  {5}
|
| Face figure | {5}
|
| Edge figure |  {3,5}
|
| Vertex figure |  {3,3,5}
|
| Dual | Self-dual |
| Coxeter group | K4, [5,3,3,5] |
| Properties | Regular |
In the geometry of hyperbolic 4-space, the order-5 120-cell honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {5,3,3,5}, it has five 120-cells around each face. It is self-dual. It also has 600 120-cells around each vertex.
Related honeycombs
[edit]It is related to the (order-3) 120-cell honeycomb, and order-4 120-cell honeycomb. It is analogous to the order-5 dodecahedral honeycomb and order-5 pentagonal tiling.
Birectified order-5 120-cell honeycomb
[edit]The birectified order-5 120-cell honeycomb constructed by all rectified 600-cells, with octahedron and icosahedron cells, and triangle faces with a 5-5 duoprism vertex figure and has extended symmetry [[5,3,3,5]].
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)