Order-5 120-cell honeycomb: Difference between revisions
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In the [[geometry]] of [[Hyperbolic space|hyperbolic 4-space]], the '''order-5 120-cell honeycomb''' is one of five compact [[regular polytope|regular]] space-filling [[tessellation]]s (or [[honeycomb (geometry)|honeycombs]]). With [[Schläfli symbol]] {5,3,3,5}, it has five [[120-cell]]s around each |
In the [[geometry]] of [[Hyperbolic space|hyperbolic 4-space]], the '''order-5 120-cell honeycomb''' is one of five compact [[regular polytope|regular]] space-filling [[tessellation]]s (or [[honeycomb (geometry)|honeycombs]]). With [[Schläfli symbol]] {5,3,3,5}, it has five [[120-cell]]s around each face. It is self-[[dual polytope|dual]]. |
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== Related honeycombs== |
== Related honeycombs== |
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Revision as of 16:22, 19 February 2015
| Order-5 120-cell honeycomb | |
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| Type | Hyperbolic regular honeycomb |
| Schläfli symbol | {5,3,3,5} |
| Coxeter diagram |    
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| 4-faces |  {5,3,3}
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| Cells |  {5,3}
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| Faces |  {5}
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| Face figure | {5}
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| Edge figure |  {3,5}
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| Vertex figure |  {3,3,5}
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| Dual | Self-dual |
| Coxeter group | K4, [5,3,3,5] |
| Properties | Regular |
In the geometry of hyperbolic 4-space, the order-5 120-cell honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {5,3,3,5}, it has five 120-cells around each face. It is self-dual.
Related honeycombs
It is related to the (order-3) 120-cell honeycomb, and order-4 120-cell honeycomb.
The birectified order-5 120-cell constructed by all rectified 600-cells, with octahedron and icosahedron cells, and triangle faces with a 5-5 duoprism vertex figure and has extended symmetry [[5,3,3,5]].
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)