# 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 | R_{6} |

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".