Small stellated 120-cell honeycomb: Difference between revisions
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!bgcolor=#e7dcc3 colspan=2|Small stellated 120-cell honeycomb |
!bgcolor=#e7dcc3 colspan=2|Small stellated 120-cell honeycomb |
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|bgcolor=#ffffff align=center colspan=2|(No image) |
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|bgcolor=#e7dcc3|Type||[[ |
|bgcolor=#e7dcc3|Type||[[List of regular polytopes#Tessellations of hyperbolic 4-space|Hyperbolic regular honeycomb]] |
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|bgcolor=#e7dcc3|[[Schläfli symbol]]||{5/2,5,3,3} |
|bgcolor=#e7dcc3|[[Schläfli symbol]]||{5/2,5,3,3} |
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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 '''small stellated 120-cell honeycomb''' is one of four [[regular polytope|regular]] star-[[honeycomb (geometry)|honeycombs]]. With [[Schläfli symbol]] {5/2,5,3,3}, it has three [[small stellated 120-cell]]s around each |
In the [[geometry]] of [[Hyperbolic space|hyperbolic 4-space]], the '''small stellated 120-cell honeycomb''' is one of four [[regular polytope|regular]] star-[[honeycomb (geometry)|honeycombs]]. With [[Schläfli symbol]] {5/2,5,3,3}, it has three [[small stellated 120-cell]]s around each face. It is [[dual polytope|dual]] to the [[pentagrammic-order 600-cell honeycomb]]. |
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It can be seen as a [[stellation]] of the [[120-cell honeycomb]], and is |
It can be seen as a [[stellation]] of the [[120-cell honeycomb]], and is thus analogous to the three-dimensional [[small stellated dodecahedron]] {5/2,5} and four-dimensional [[small stellated 120-cell]] {5/2,5,3}. It has [[density (polytope)|density]] 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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[[Category:5-polytopes]] |
[[Category:5-polytopes]] |
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Latest revision as of 23:23, 12 May 2024
 | This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. (May 2024) |
| Small stellated 120-cell honeycomb | |
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| (No image) | |
| Type | Hyperbolic regular honeycomb |
| Schläfli symbol | {5/2,5,3,3} |
| Coxeter diagram |      
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| 4-faces |  {5/2,5,3}
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| Cells |  {5/2,5}
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| Faces |  {5/2}
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| Face figure |  {3}
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| Edge figure |  {3,3}
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| Vertex figure |  {5,3,3}
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| Dual | Pentagrammic-order 600-cell honeycomb |
| Coxeter group | H4, [5,3,3,3] |
| Properties | Regular |
In the geometry of hyperbolic 4-space, the small stellated 120-cell honeycomb is one of four regular star-honeycombs. With Schläfli symbol {5/2,5,3,3}, it has three small stellated 120-cells around each face. It is dual to the pentagrammic-order 600-cell honeycomb.
It can be seen as a stellation of the 120-cell honeycomb, and is thus analogous to the three-dimensional small stellated dodecahedron {5/2,5} and four-dimensional small stellated 120-cell {5/2,5,3}. It has density 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)
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