| 5-cubic honeycomb | |
|---|---|
| (no image) | |
| Type | Regular 5-space honeycomb |
| Family | Hypercube honeycomb |
| Schläfli symbol | {4,3,3,3,4} t0,5{4,3,3,3,4} {4,3,3,31,1} {4,3,4}x{∞} {4,3,4}x{4,4} {4,3,4}x{∞}2 {4,4}2x{∞} {∞}5 |
| Coxeter-Dynkin diagrams | |
| 5-face type | {4,3,3,3} |
| 4-face type | {4,3,3} |
| Cell type | {4,3} |
| Face type | {4} |
| Face figure | {4,3} (octahedron) |
| Edge figure | 8 {4,3,3} (16-cell) |
| Vertex figure | 32 {4,3,3,3} (pentacross) |
| Coxeter group | [4,3,3,3,4] |
| Dual | self-dual |
| Properties | vertex-transitive, edge-transitive, face-transitive, cell-transitive |
The 5-cubic honeycomb or penteractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 5-space. Four 5-cubes meet at each cubic cell, and it is more explicitly called an order-4 penteractic honeycomb.
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 {4,3,3,3,4}. Another form has two alternating 5-cube facets (like a checkerboard) with Schläfli symbol {4,3,3,31,1}. The lowest symmetry Wythoff construction has 32 types of facets around each vertex and a prismatic product Schläfli symbol {∞}5.
It is also related to the regular 6-cube which exists in 6-space with 3 5-cubes on each cell. This could be considered as a tessellation on the 5-sphere, an order-3 penteractic honeycomb, {4,3,3,3,3}.