Order-5 5-cell honeycomb
{{Short description|Compact regular space-filling tessellation}}
{{No footnotes|date=March 2025}}
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!bgcolor=#e7dcc3 colspan=2|Order-5 5-cell honeycomb | |
| bgcolor=#ffffff align=center colspan=2|(No image) | |
| bgcolor=#e7dcc3|Type | Hyperbolic regular honeycomb |
| bgcolor=#e7dcc3|Schläfli symbol | {3,3,3,5} |
| bgcolor=#e7dcc3|Coxeter diagram | {{CDD|node_1|3|node|3|node|3|node|5|node}} |
| bgcolor=#e7dcc3|4-faces | 50px {3,3,3} |
| bgcolor=#e7dcc3|Cells | 30px {3,3} |
| bgcolor=#e7dcc3|Faces | 30px {3} |
| bgcolor=#e7dcc3|Face figure | 30px {5} |
| bgcolor=#e7dcc3|Edge figure | 30px {3,5} |
| bgcolor=#e7dcc3|Vertex figure | 50px {3,3,5} |
| bgcolor=#e7dcc3|Dual | 120-cell honeycomb |
| bgcolor=#e7dcc3|Coxeter group | {{overline|H}}4, [5,3,3,3] |
| bgcolor=#e7dcc3|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
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
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)