Order-5 icosahedral 120-cell honeycomb
| Order-5 icosahedral 120-cell honeycomb | |
|---|---|
| (No image) | |
| Type | Hyperbolic regular honeycomb |
| Schläfli symbol | {3,5,5/2,5} |
| Coxeter diagram |       |
| 4-faces |  {3,5,5/2} |
| Cells |  {3,5} |
| Faces |  {3} |
| Face figure |  {5} |
| Edge figure |  {5/2,5} |
| Vertex figure |  {5,5/2,5} |
| Dual | Great 120-cell honeycomb |
| Coxeter group | H4, [5,3,3,3] |
| Properties | Regular |
In the geometry of hyperbolic 4-space, the order-5 icosahedral 120-cell honeycomb is one of four regular star-honeycombs. With Schläfli symbol {3,5,5/2,5}, it has five icosahedral 120-cells around each face. It is dual to the great 120-cell honeycomb.
It can be constructed by replacing the great dodecahedral cells of the great 120-cell honeycomb with their icosahedral convex hulls, thus replacing the great 120-cells with icosahedral 120-cells. It is thus analogous to the four-dimensional icosahedral 120-cell. It has density 10.
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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