120-cell honeycomb explained
| bgcolor=#e7dcc3 colspan=2 | 120-cell honeycomb |
|---|
| bgcolor=#ffffff align=center colspan=2 | (No image) |
| Type | Hyperbolic regular honeycomb |
| Schläfli symbol | |
| Coxeter diagram | |
| 4-faces | |
| Cells | |
| Faces | |
| Face figure | |
| Edge figure | |
| Vertex figure | |
| Dual | Order-5 5-cell honeycomb |
| Coxeter group | 4, [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, it has three
120-cells around each face. Its dual is the
order-5 5-cell honeycomb, .
Related honeycombs
It is related to the order-4 120-cell honeycomb,, and order-5 120-cell honeycomb, .
It is topologically similar to the finite 5-cube,, and 5-simplex, .
It is analogous to the 120-cell,, and dodecahedron, .
See also
References
- Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
- Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II, III, IV, V, p212-213)
