120-cell honeycomb
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. Its dual is the order-5 5-cell honeycomb, {3,3,3,5}.
| 120-cell honeycomb | |
|---|---|
| (No image) | |
| Type | Hyperbolic regular honeycomb |
| Schläfli symbol | {5,3,3,3} |
| Coxeter diagram |     |
| 4-faces |  {5,3,3} |
| Cells |  {5,3} |
| Faces |  {5} |
| Face figure |  {3} |
| Edge figure |  {3,3} |
| Vertex figure |  {3,3,3} |
| Dual | Order-5 5-cell honeycomb |
| Coxeter group | H4, [5,3,3,3] |
| Properties | Regular |
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
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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