Order-5 5-cell honeycomb
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Short description: Compact regular space-filling tessellation
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| Order-5 5-cell honeycomb | |
|---|---|
| (No image) | |
| Type | Hyperbolic regular honeycomb |
| Schläfli symbol | {3,3,3,5} |
| Coxeter diagram |    
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| 4-faces | 50px {3,3,3} |
| Cells | 30px {3,3} |
| Faces | 30px {3} |
| Face figure | 30px {5} |
| Edge figure | 30px {3,5} |
| Vertex figure | 50px {3,3,5} |
| Dual | 120-cell honeycomb |
| Coxeter group | H4, [5,3,3,3] |
| Properties | Regular |
In the geometry of hyperbolic 4-space, the order-5 5-cell honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {3,3,3,5}, it has five 5-cells around each face. Acronym: pente[1]
Its dual is the 120-cell honeycomb, {5,3,3,3}.
Related honeycombs
It is related to the order-5 tesseractic honeycomb, {4,3,3,5}, and order-5 120-cell honeycomb, {5,3,3,5}.
It is topologically similar to the finite 5-orthoplex, {3,3,3,4}, and 5-simplex, {3,3,3,3}.
It is analogous to the 600-cell, {3,3,5}, and icosahedron, {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. x3o3o3o5o - pente
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