Order-5 tesseractic honeycomb
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!bgcolor=#e7dcc3 colspan=2|Order-5 tesseractic honeycomb | |
| bgcolor=#ffffff align=center colspan=2|(No image) | |
| bgcolor=#e7dcc3|Type | Hyperbolic regular honeycomb |
| bgcolor=#e7dcc3|Schläfli symbol | {4,3,3,5} |
| bgcolor=#e7dcc3|Coxeter diagram | {{CDD|node_1|4|node|3|node|3|node|5|node}} |
| bgcolor=#e7dcc3|4-faces | 50px {4,3,3} |
| bgcolor=#e7dcc3|Cells | 30px {4,3} |
| bgcolor=#e7dcc3|Faces | 30px {4} |
| bgcolor=#e7dcc3|Face figure | 30px {5} |
| bgcolor=#e7dcc3|Edge figure | 30px {3,5} |
| bgcolor=#e7dcc3|Vertex figure | 50px {3,3,5} |
| bgcolor=#e7dcc3|Dual | Order-4 120-cell honeycomb |
| bgcolor=#e7dcc3|Coxeter group | {{overline|BH}}4, [5,3,3,4] |
| bgcolor=#e7dcc3|Properties | Regular |
In the geometry of hyperbolic 4-space, the order-5 tesseractic honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {4,3,3,5}, it has five 8-cells (also known as tesseracts) around each face. Its dual is the order-4 120-cell honeycomb, {5,3,3,4}.
Related polytopes and honeycombs
It is related to the Euclidean 4-space (order-4) tesseractic honeycomb, {4,3,3,4}, and the 5-cube, {4,3,3,3} in Euclidean 5-space. The 5-cube can also be seen as an order-3 tesseractic honeycomb on the surface of a 4-sphere.
See also
References
- 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)