Penteractic pentacomb
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| 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 |
| Abstract & topological properties | |
| Orientable | Yes |
| Properties | |
| Symmetry | R6 |
| Convex | Yes |
| Nature | Tame |
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.
Vertex coordinates[edit | edit source]
The vertices of a penteractic pentacomb of edge length 1 are given by
- ,
where i , j , k , l , m are integers.
Representations[edit | edit source]
A penteractic pentacomb has the following Coxeter diagrams:
- x4o3o3o3o4o () (full symmetry)
- o3o3o3o4x *b3o (
) (half symmetry)
External links[edit | edit source]
- Klitzing, Richard. "penth".
- Wikipedia contributors. "5-cubic honeycomb".