120-cell honeycomb
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Short description: 5-dimensional regular honeycomb
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| 120-cell honeycomb | |
|---|---|
| (No image) | |
| Type | Hyperbolic regular honeycomb |
| Schläfli symbol | {5,3,3,3} |
| Coxeter diagram |    
|
| 4-faces | 50px {5,3,3} |
| Cells | 30px {5,3} |
| Faces | 30px {5} |
| Face figure | 30px {3} |
| Edge figure | 30px {3,3} |
| Vertex figure | 50px {3,3,3} |
| Dual | Order-5 5-cell honeycomb |
| Coxeter group | H4, [5,3,3,3] |
| Properties | Regular |
In the geometry of hyperbolic 4-space, the 120-cell honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {5,3,3,3}, it has three 120-cells around each face. Acronym: hitte[1]
Its dual is the order-5 5-cell honeycomb, {3,3,3,5}.
Related honeycombs
It is related to the order-4 120-cell honeycomb, {5,3,3,4}, and order-5 120-cell honeycomb, {5,3,3,5}.
It is topologically similar to the finite 5-cube, {4,3,3,3}, and 5-simplex, {3,3,3,3}.
It is analogous to the 120-cell, {5,3,3}, and dodecahedron, {5,3}.
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. o3o3o3o5x - hitte
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