Order-5 120-cell honeycomb
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| Order-5 120-cell honeycomb | |
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| (No image) | |
| Type | Hyperbolic regular honeycomb |
| Schläfli symbol | {5,3,3,5} |
| Coxeter diagram |    
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| 4-faces |  {5,3,3}
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| Cells |  {5,3}
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| Faces |  {5}
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| Face figure | {5}
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| Edge figure |  {3,5}
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| Vertex figure |  {3,3,5}
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| 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
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
- List of regular polytopes
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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