Order-5 5-cell honeycomb: Difference between revisions
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|bgcolor=#e7dcc3|Type||[[ |
|bgcolor=#e7dcc3|Type||[[List of regular polytopes#Tessellations of hyperbolic 3-space|Hyperbolic regular honeycomb]] |
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|bgcolor=#e7dcc3|[[Schläfli symbol]]||{3,3,3,5} |
|bgcolor=#e7dcc3|[[Schläfli symbol]]||{3,3,3,5} |
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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 face. Its [[dual polytope|dual]] is the [[120-cell honeycomb]], {5,3,3,3}. |
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 face. Its [[dual polytope|dual]] is the [[120-cell honeycomb]], {5,3,3,3}. |
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== Related honeycombs== |
== Related honeycombs== |
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It is related to the [[order-5 tesseractic honeycomb]], {4,3,3,5}, and [[order-5 120-cell honeycomb]], {5,3,3,5}. |
It is related to the [[order-5 tesseractic honeycomb]], {4,3,3,5}, and [[order-5 120-cell honeycomb]], {5,3,3,5}. |
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It is topologically similar to the finite [[5-orthoplex]], {3,3,3,4}, and [[5-simplex]], {3,3,3,3}. |
It is topologically similar to the finite [[5-orthoplex]], {3,3,3,4}, and [[5-simplex]], {3,3,3,3}. |
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It is analogous to the [[600-cell]] {3,3,5} and [[icosahedron]] {3,5}. |
It is analogous to the [[600-cell]], {3,3,5}, and [[icosahedron]], {3,5}. |
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== See also == |
== See also == |
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== References == |
== References == |
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*[[H.S.M. Coxeter|Coxeter]], ''[[Regular Polytopes (book)|Regular Polytopes]]'', 3rd. ed., Dover Publications, 1973. |
*[[H.S.M. Coxeter|Coxeter]], ''[[Regular Polytopes (book)|Regular Polytopes]]'', 3rd. ed., Dover Publications, 1973. {{isbn|0-486-61480-8}}. (Tables I and II: Regular polytopes and honeycombs, pp. 294–296) |
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*[[H.S.M. Coxeter|Coxeter]], ''The Beauty of Geometry: Twelve Essays'', Dover Publications, 1999 |
*[[H.S.M. Coxeter|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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[[Category:Honeycombs (geometry)]] |
[[Category:Honeycombs (geometry)]] |
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Latest revision as of 00:14, 28 January 2024
| 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 face. Its dual is the 120-cell honeycomb, {5,3,3,3}.
Related honeycombs
[edit]It is related to the order-5 tesseractic honeycomb, {4,3,3,5}, and order-5 120-cell honeycomb, {5,3,3,5}.
It is topologically similar to the finite 5-orthoplex, {3,3,3,4}, and 5-simplex, {3,3,3,3}.
It is analogous to the 600-cell, {3,3,5}, and icosahedron, {3,5}.
See also
[edit]References
[edit]- 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)