| bgcolor=#e7dcc3 colspan=2 | 8-cubic honeycomb | |
|---|---|---|
| bgcolor=#ffffff align=center colspan=2 | (no image) | |
| Type | Regular 8-honeycomb Uniform 8-honeycomb | |
| Family | Hypercube honeycomb | |
| Schläfli symbol | t0,8 (8) | |
| Coxeter-Dynkin diagrams | ||
| 8-face type | ||
| 7-face type | ||
| 6-face type | ||
| 5-face type | ||
| 4-face type | ||
| Cell type | ||
| Face type | ||
| Face figure | (octahedron) | |
| Edge figure | 8 (16-cell) | |
| Vertex figure | 256 (8-orthoplex) | |
| Coxeter group | [4,3<sup>6</sup>,4] | |
| Dual | self-dual | |
| Properties | vertex-transitive, edge-transitive, face-transitive, cell-transitive |
It is analogous to the square tiling of the plane and to the cubic honeycomb of 3-space, and the tesseractic honeycomb of 4-space.
There are many different Wythoff constructions of this honeycomb. The most symmetric form is regular, with Schläfli symbol . Another form has two alternating hypercube facets (like a checkerboard) with Schläfli symbol . The lowest symmetry Wythoff construction has 256 types of facets around each vertex and a prismatic product Schläfli symbol (8).
The [4,3<sup>6</sup>,4],, Coxeter group generates 511 permutations of uniform tessellations, 271 with unique symmetry and 270 with unique geometry. The expanded 8-cubic honeycomb is geometrically identical to the 8-cubic honeycomb.
The 8-cubic honeycomb can be alternated into the 8-demicubic honeycomb, replacing the 8-cubes with 8-demicubes, and the alternated gaps are filled by 8-orthoplex facets.
A quadrirectified 8-cubic honeycomb,, contains all trirectified 8-orthoplex facets and is the Voronoi tessellation of the D8* lattice. Facets can be identically colored from a doubled
{\tilde{C}}8
{\tilde{C}}8
{\tilde{B}}8
{\tilde{D}}8