# Penteractic pentacomb

Penteractic pentacomb
Rank6
TypeRegular
SpaceEuclidean
Notation
Bowers style acronymPenth
Coxeter diagramx4o3o3o3o4o ()
Schläfli symbol{4,3,3,3,4}
Elements
PetaN penteracts
Tera5N tesseracts
Cells10N cubes
Faces10N squares
Edges5N
VerticesN
Vertex figureTriacontaditeron, edge length 2
Related polytopes
ArmyPenth
RegimentPenth
DualPenteractic pentacomb
ConjugateNone
Topological properties
OrientableYes
Properties
SymmetryR6
ConvexYes

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)