# Muoctahedron

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Muoctahedron | |
---|---|

Rank | 3 |

Space | Euclidean |

Notation | |

Schläfli symbol | |

Elements | |

Faces | 2N hexagons |

Edges | 6N |

Vertices | 3N |

Related polytopes | |

Army | Batch |

Regiment | Batch |

Dual | Mucube |

Petrie dual | Petrial muoctahedron |

Convex hull | Bitruncated cubic honeycomb |

Abstract properties | |

Schläfli type | {6,4} |

Topological properties | |

Orientable | Yes |

Genus | ∞ |

Properties | |

Symmetry | R_{4}×2 |

Convex | No |

The **muoctahedron** or **muo**, short for multiple octahedron, is one of the three regular skew apeirohedra in Euclidean 3-space. It’s an infinite polyhedron that consists solely of hexagons, with 4 meeting at each vertex.

The muoctahedron is based on the bitruncated cubic honeycomb. Its faces are the hexagonal faces of the bitruncated cubic honeycomb.

It can also be formed as a modwrap of the order-4 hexagonal tiling by identifying every 4th vertex on each hole.

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the bitruncated cubic honeycomb.

## External links[edit | edit source]

- Wikipedia Contributors. "Regular skew apeirohedron".
- Klitzing, Richard. "shexat".

- Klitzing, Richard. "Skew polytopes".

## References[edit | edit source]

- Conway, John H.; Burgiel, Heidi; Goodman-Strauss, Chaim (2008).
*The Symmetries of Things*. pp. 333–335. - Coxeter, H.S.M. (1999).
*The Beauty of Geometry: Twelve essays*. Dover Publications, Inc. pp. 157*ff*. - McMullen, Peter; Schulte, Egon (1997). "Regular Polytopes in Ordinary Space".
*Discrete Computational Geometry*.**17**: 449–478. - jan Misali (2020). "there are 48 regular polyhedra".