# Mucubic honeycomb

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Mucubic honeycomb | |
---|---|

Rank | 4 |

Type | Regular |

Space | Euclidean |

Notation | |

Schläfli symbol | |

Elements | |

Cells | 4 mucubes |

Faces | 3n squares |

Edges | 3n |

Vertices | n |

Vertex figure | Petrial octahedron, edge length √2 |

Related polytopes | |

Army | Chon |

Regiment | Chon |

Petrie dual | Cubic honeycomb |

Abstract properties | |

Schläfli type | {4,6,4} |

Properties | |

Symmetry | R_{4} |

Convex | No |

The **mucubic honeycomb** or **petrial cubic honeycomb** is a regular skew polychoron consisting of 4 mucubes. It shares its faces, edges, and vertices with the cubic honeycomb, and it has a petrial octahedron vertex figure. It is also the Petrie dual of the cubic honeycomb.^{[1]}

## Vertex coordinates[edit | edit source]

The vertex coordinates of the mucubic honeycomb are the same as that of its regiment colonel, the cubic honeycomb.

## External links[edit | edit source]

- McMullen, Peter; Schulte, Egon (1997). "Regular Polytopes in Ordinary Space" (PDF).
*Discrete Computational Geometry*(47): 449–478. doi:10.1007/PL00009304.

## References[edit | edit source]

- ↑ McMullen, Peter (2004). "Regular Polytopes of Full Rank" (PDF).
*Discrete Computational Geometry*: 20.