Order-5 cubic honeycomb
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| Order-5 cubic honeycomb | |
|---|---|
  Poincaré disk models |
|
| Type | Hyperbolic regular honeycomb |
| Schläfli symbol | {4,3,5} |
| Coxeter-Dynkin diagram |      |
| Cells | cube {4,3} |
| Faces | square {4} |
| Edge figure | pentagon {5} |
| Vertex figure | icosahedron {3,5} |
| Cells/edge | {4,3}5 |
| Cells/vertex | {4,3}20 |
| Euler characteristic | 0 |
| Coxeter group | [5,3,4] |
| Dual | Order-4 dodecahedral honeycomb |
| Properties | Regular |
The order-5 cubic honeycomb is one of four space-filling tessellations (or honeycombs) in hyperbolic 3-space.
In this honeycomb, five cubes exist on each edge, and 20 cubes around each vertex. It is dual with the order-4 dodecahedral honeycomb.
It is related to the regular (order-4) cubic honeycomb of Euclidean 3-space, which has 4 cubes per edge, and also the tesseract of Euclidean 4-space with 3 cubes per edge.
[edit] 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, p212-213)
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