Order-5 5-cell honeycomb: Difference between revisions
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|bgcolor=#e7dcc3|Face figure||[[File:Regular_polygon_5_annotated.svg|30px]] [[Pentagon|{5}]] |
|bgcolor=#e7dcc3|Face figure||[[File:Regular_polygon_5_annotated.svg|30px]] [[Pentagon|{5}]] |
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|bgcolor=#e7dcc3|Edge figure||[[File: |
|bgcolor=#e7dcc3|Edge figure||[[File:Icosahedron.svg|30px]] [[Icosahedron|{3,5}]] |
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|bgcolor=#e7dcc3|[[Vertex figure]]||[[File:Schlegel_wireframe_600-cell.png|50px]] [[600-cell|{3,3,5}]] |
|bgcolor=#e7dcc3|[[Vertex figure]]||[[File:Schlegel_wireframe_600-cell.png|50px]] [[600-cell|{3,3,5}]] |
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|bgcolor=#e7dcc3|Properties||Regular |
|bgcolor=#e7dcc3|Properties||Regular |
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In the [[geometry]] of [[Hyperbolic space|hyperbolic 4-space]], the ''' |
In the [[geometry]] of [[Hyperbolic space|hyperbolic 4-space]], the '''order-5 5-cell honeycomb''' is one of five compact [[regular polytope|regular]] space-filling [[tessellation]]s (or [[honeycomb (geometry)|honeycombs]]). With [[Schläfli symbol]] {3,3,3,5}, it has five [[5-cell]]s around each edge. Its [[dual polytope|dual]] is the [[120-cell honeycomb]], {5,3,3,3}. |
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== See also == |
== See also == |
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Revision as of 00:14, 13 February 2014
| Order-5 5-cell honeycomb | |
|---|---|
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| Type | Hyperbolic regular honeycomb |
| Schläfli symbol | {3,3,3,5} |
| Coxeter diagram |    
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| 4-faces |  {3,3,3}
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| Cells |  {3,3}
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| Faces |  {3}
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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 | 120-cell honeycomb |
| Coxeter group | H4, [5,3,3,3] |
| Properties | Regular |
In the geometry of hyperbolic 4-space, the order-5 5-cell honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {3,3,3,5}, it has five 5-cells around each edge. Its dual is the 120-cell honeycomb, {5,3,3,3}.
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)