Order-5 120-cell honeycomb
From HandWiki
Short description: 5-dimensional regular honeycomb
 | This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. (July 2026) (Learn how and when to remove this template message) |
| Order-5 120-cell honeycomb | |
|---|---|
| (No image) | |
| Type | Hyperbolic regular honeycomb |
| Schläfli symbol | {5,3,3,5} |
| Coxeter diagram |    
|
| 4-faces | 50px {5,3,3} |
| Cells | 30px {5,3} |
| Faces | 30px {5} |
| Face figure | 30px {5} |
| Edge figure | 30px {3,5} |
| Vertex figure | 50px {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. Acronym: phitte[1]
It is self-dual. It also has 600 120-cells around each vertex.
Related honeycombs
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
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
Notes
References
- 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, pp. 212–213)
- Klitzing, Richard. "4D Tetracombs". https://bendwavy.org/klitzing/dimensions/hyperbolic.htm#4D-compact. x5o3o3o5o - phitte
 |  |
