Octeractic octacomb
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| Octeractic octacomb | |
|---|---|
| (no image) | |
| Type | Regular octacomb |
| Family | Hypercube honeycomb |
| Schläfli symbol | {4,36,4} {4,35,31,1} {∞}8 |
| Coxeter-Dynkin diagrams |            ... |
| 8-face type | {4,36} |
| 7-face type | {4,35} |
| 6-face type | {4,34} |
| 5-face type | {4,33} |
| 4-face type | {4,32} |
| Cell type | {4,3} |
| Face type | {4} |
| Face figure | {4,3} (octahedron) |
| Edge figure | 8 {4,3,3} (16-cell) |
| Vertex figure | 256 {4,36} (octacross) |
| Coxeter group | [4,36,4] |
| Dual | self-dual |
| Properties | vertex-transitive, edge-transitive, face-transitive, cell-transitive |
The octeractic octacomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 8-space.
It is an analog of the square tiling of the plane, the cubic honeycomb of 3-space.
There are many different Wythoff constructions of this honeycomb. The most symmetric form is regular, with Schläfli symbol {4,36,4}. Another form has two alternating hypercube facets (like a checkerboard) with Schläfli symbol {4,35,31,1}. The lowest symmetry Wythoff construction has 256 types of facets around each vertex and a prismatic product Schläfli symbol {∞}8.
[edit] See also
- Tesseractic tetracomb
- Penteractic pentacomb
- Hexeractic hexacomb
- Hepteractic heptacomb
- List of regular polytopes
[edit] References
- Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8 p.296, Table II: Regular honeycombs
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