Order-5 icosahedral 120-cell honeycomb: Difference between revisions
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!bgcolor=#e7dcc3 colspan=2|Order-5 icosahedral 120-cell honeycomb |
!bgcolor=#e7dcc3 colspan=2|Order-5 icosahedral 120-cell honeycomb |
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|bgcolor=#ffffff align=center colspan=2|(No image) |
|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]]||{3,5,5/2,5} |
|bgcolor=#e7dcc3|[[Schläfli symbol]]||{3,5,5/2,5} |
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|bgcolor=#e7dcc3|[[Coxeter diagram]]||{{CDD|node_1|3|node|5|node|5|rat|2x|node|5|node}} |
|bgcolor=#e7dcc3|[[Coxeter diagram]]||{{CDD|node_1|3|node|5|node|5|rat|2x|node|5|node}} |
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|bgcolor=#e7dcc3|4-faces||[[File:Ortho solid |
|bgcolor=#e7dcc3|4-faces||[[File:Ortho solid 007-uniform polychoron 35p-t0.png|50px]] [[Icosahedral 120-cell|{3,5,5/2}]] |
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|bgcolor=#e7dcc3|Cells||[[File:Icosahedron.png|30px]] [[Icosahedron|{3,5}]] |
|bgcolor=#e7dcc3|Cells||[[File:Icosahedron.png|30px]] [[Icosahedron|{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 '''order-5 icosahedral 120-cell honeycomb''' is one of four [[regular polytope|regular]] star-[[honeycomb (geometry)|honeycombs]]. With [[Schläfli symbol]] {3,5,5/2,5}, it has five [[ |
In the [[geometry]] of [[Hyperbolic space|hyperbolic 4-space]], the '''order-5 icosahedral 120-cell honeycomb''' is one of four [[regular polytope|regular]] star-[[honeycomb (geometry)|honeycombs]]. With [[Schläfli symbol]] {3,5,5/2,5}, it has five [[icosahedral 120-cell]]s around each face. It is [[dual polytope|dual]] to the [[great 120-cell honeycomb]]. |
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It can be constructed by replacing the [[great dodecahedron|great dodecahedral]] cells of the great 120-cell honeycomb with their [[regular icosahedron|icosahedral]] convex hulls, thus replacing the [[great 120-cell]]s with [[icosahedral 120-cell]]s. It is thus analogous to the four-dimensional [[icosahedral 120-cell]]. It has [[density (polytope)|density]] 10. |
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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]] |
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Latest revision as of 16:49, 3 August 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) |
| Order-5 icosahedral 120-cell honeycomb | |
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| Type | Hyperbolic regular honeycomb |
| Schläfli symbol | {3,5,5/2,5} |
| Coxeter diagram |      
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| 4-faces |  {3,5,5/2}
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| Cells |  {3,5}
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| Faces |  {3}
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| Face figure |  {5}
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| Edge figure |  {5/2,5}
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| Vertex figure |  {5,5/2,5}
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| Dual | Great 120-cell honeycomb |
| Coxeter group | H4, [5,3,3,3] |
| Properties | Regular |
In the geometry of hyperbolic 4-space, the order-5 icosahedral 120-cell honeycomb is one of four regular star-honeycombs. With Schläfli symbol {3,5,5/2,5}, it has five icosahedral 120-cells around each face. It is dual to the great 120-cell honeycomb.
It can be constructed by replacing the great dodecahedral cells of the great 120-cell honeycomb with their icosahedral convex hulls, thus replacing the great 120-cells with icosahedral 120-cells. It is thus analogous to the four-dimensional icosahedral 120-cell. It has density 10.
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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