Penteractic pentacomb

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

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

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.

Representations

A penteractic pentacomb has the following Coxeter diagrams:

• x4o3o3o3o4o (full symmetry)
• o3o3o *b3o3o4x (half symmetry)

External links

• Klitzing, Richard. "penth".

• Wikipedia Contributors. "5-cubic honeycomb".