Great 120-cell honeycomb: Difference between revisions
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{| class="wikitable" align="right" style="margin-left:10px" width=" |
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!bgcolor=#e7dcc3 colspan=2| |
!bgcolor=#e7dcc3 colspan=2|Great 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]]||{5,5/2,5,3} |
|bgcolor=#e7dcc3|[[Schläfli symbol]]||{5,5/2,5,3} |
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|bgcolor=#e7dcc3|[[Coxeter diagram]]||{{CDD|node_1|5|node|5|rat|2x|node|5|node|3|node}} |
|bgcolor=#e7dcc3|[[Coxeter diagram]]||{{CDD|node_1|5|node|5|rat|2x|node|5|node|3|node}} |
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|bgcolor=#e7dcc3|4-faces||[[File: |
|bgcolor=#e7dcc3|4-faces||[[File:Ortho_solid_008-uniform_polychoron_5p5-t0.png|50px]] [[Great 120-cell|{5,5/2,5}]] |
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|bgcolor=#e7dcc3|Cells||[[File: |
|bgcolor=#e7dcc3|Cells||[[File:Great dodecahedron.png|30px]] [[Great dodecahedron|{5,5/2}]] |
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|bgcolor=#e7dcc3|Faces||[[File:Regular_polygon_5_annotated.svg|30px]] [[Pentagon|{5}]] |
|bgcolor=#e7dcc3|Faces||[[File:Regular_polygon_5_annotated.svg|30px]] [[Pentagon|{5}]] |
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|bgcolor=#e7dcc3|Face figure||[[File:Regular_polygon_3_annotated.svg|30px]] [[Triangle|{3}]] |
|bgcolor=#e7dcc3|Face figure||[[File:Regular_polygon_3_annotated.svg|30px]] [[Triangle|{3}]] |
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|bgcolor=#e7dcc3|Edge figure||[[File: |
|bgcolor=#e7dcc3|Edge figure||[[File:dodecahedron.png|30px]] [[dodecahedron|{5,3}]] |
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|bgcolor=#e7dcc3|[[Vertex figure]]||[[File:Ortho solid |
|bgcolor=#e7dcc3|[[Vertex figure]]||[[File:Ortho solid 010-uniform polychoron p53-t0.png|50px]] [[Small stellated 120-cell|{5/2,5,3}]] |
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|bgcolor=#e7dcc3|Dual||[[ |
|bgcolor=#e7dcc3|Dual||[[Order-5 icosahedral 120-cell honeycomb]] |
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|bgcolor=#e7dcc3|[[Coxeter group]]||{{overline|H}}<sub>4</sub>, [5,3,3,3] |
|bgcolor=#e7dcc3|[[Coxeter group]]||{{overline|H}}<sub>4</sub>, [5,3,3,3] |
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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 ''' |
In the [[geometry]] of [[Hyperbolic space|hyperbolic 4-space]], the '''great 120-cell honeycomb''' is one of four [[regular polytope|regular]] star-[[honeycomb (geometry)|honeycombs]]. With [[Schläfli symbol]] {5,5/2,5,3}, it has three [[great 120-cell]]s around each face. It is [[dual polytope|dual]] to the [[order-5 icosahedral 120-cell honeycomb]]. |
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It can be seen as a [[stellation#Naming stellations|greatening]] of the [[120-cell honeycomb]], and is thus analogous to the three-dimensional [[great dodecahedron]] {5,5/2} and four-dimensional [[great 120-cell]] {5,5/2,5}. 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. ISBN |
*[[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 ISBN |
*[[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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{{geometry-stub}} |
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Latest revision as of 21:31, 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) |
| Great 120-cell honeycomb | |
|---|---|
| (No image) | |
| Type | Hyperbolic regular honeycomb |
| Schläfli symbol | {5,5/2,5,3} |
| Coxeter diagram |      
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| 4-faces |  {5,5/2,5}
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| Cells |  {5,5/2}
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| Faces |  {5}
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| Face figure |  {3}
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| Edge figure |  {5,3}
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| Vertex figure |  {5/2,5,3}
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| Dual | Order-5 icosahedral 120-cell honeycomb |
| Coxeter group | H4, [5,3,3,3] |
| Properties | Regular |
In the geometry of hyperbolic 4-space, the great 120-cell honeycomb is one of four regular star-honeycombs. With Schläfli symbol {5,5/2,5,3}, it has three great 120-cells around each face. It is dual to the order-5 icosahedral 120-cell honeycomb.
It can be seen as a greatening of the 120-cell honeycomb, and is thus analogous to the three-dimensional great dodecahedron {5,5/2} and four-dimensional great 120-cell {5,5/2,5}. 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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