Great 120-cell honeycomb: Difference between revisions
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In the [[geometry]] of [[Hyperbolic space|hyperbolic 4-space]], the '''great 120-cell honeycomb''' is one of four [[regular polytope|regular]] star-[[honeycomb (geometry)|honeycombs]]. With [[Schläfli symbol]] {5,5/2,5,3}, it has three [[great 120-cell]]s around each |
In the [[geometry]] of [[Hyperbolic space|hyperbolic 4-space]], the '''great 120-cell honeycomb''' is one of four [[regular polytope|regular]] star-[[honeycomb (geometry)|honeycombs]]. With [[Schläfli symbol]] {5,5/2,5,3}, it has three [[great 120-cell]]s around each face. It is [[dual polytope|dual]] to the [[order-5 icosahedral 120-cell honeycomb]]. |
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It can be seen as a [[stellation#Naming stellations|greatening]] of the [[120-cell honeycomb]], and is thus analogous to the three-dimensional [[great dodecahedron]] {5,5/2} and four-dimensional [[great 120-cell]] {5,5/2,5}. It has [[density (polytope)|density]] 10. |
It can be seen as a [[stellation#Naming stellations|greatening]] of the [[120-cell honeycomb]], and is thus analogous to the three-dimensional [[great dodecahedron]] {5,5/2} and four-dimensional [[great 120-cell]] {5,5/2,5}. It has [[density (polytope)|density]] 10. |
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Revision as of 16:25, 19 February 2015
| Great 120-cell honeycomb | |
|---|---|
| (No image) | |
| Type | Hyperbolic regular honeycomb |
| Schläfli symbol | {5,5/2,5,3} |
| Coxeter diagram |      
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| 4-faces |  {5,5/2,5}
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| Cells |  {5,5/2}
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| Faces |  {5}
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| Face figure |  {3}
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| Edge figure |  {5,3}
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| Vertex figure |  {5/2,5,3}
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| Dual | Order-5 icosahedral 120-cell honeycomb |
| Coxeter group | H4, [5,3,3,3] |
| Properties | Regular |
In the geometry of hyperbolic 4-space, the great 120-cell honeycomb is one of four regular star-honeycombs. With Schläfli symbol {5,5/2,5,3}, it has three great 120-cells around each face. It is dual to the order-5 icosahedral 120-cell honeycomb.
It can be seen as a greatening of the 120-cell honeycomb, and is thus analogous to the three-dimensional great dodecahedron {5,5/2} and four-dimensional great 120-cell {5,5/2,5}. 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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