Penteractic pentacomb
The penteractic pentacomb or penth, also called the penteractic honeycomb or 5-cubic honeycomb, is the only regular pentacomb or tessellation of 5D Euclidean space. 4 penteracts join at each cell, and 32 join at each vertex of this honeycomb. It is the 5D hypercubic honeycomb.
| Penteractic pentacomb | |
|---|---|
| Rank | 6 |
| Type | Regular |
| Space | Euclidean |
| Notation | |
| Bowers style acronym | Penth |
| Coxeter diagram | x4o3o3o3o4o (    ) |
| Schläfli symbol | {4,3,3,3,4} |
| Elements | |
| Peta | N penteracts |
| Tera | 5N tesseracts |
| Cells | 10N cubes |
| Faces | 10N squares |
| Edges | 5N |
| Vertices | N |
| Vertex figure | Triacontaditeron, edge length √2 |
| Related polytopes | |
| Army | Penth |
| Regiment | Penth |
| Dual | Penteractic pentacomb |
| Conjugate | None |
| Topological properties | |
| Orientable | Yes |
| Properties | |
| Symmetry | R6 |
| Convex | Yes |
Vertex coordinatesEdit
The vertices of a penteractic pentacomb of edge length 1 are given by (i, j, k, l, m), where i, j, k, l, m are integers.
RepresentationsEdit
A penteractic pentacomb has the following Coxeter diagrams:
- x4o3o3o3o4o (full symmetry)
- o3o3o *b3o3o4x (half symmetry)
External linksEdit
- Klitzing, Richard. "penth".
- Wikipedia Contributors. "5-cubic honeycomb".