# Truncated tetrahedral-octahedral honeycomb

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Truncated tetrahedral-octahedral honeycomb | |
---|---|

Rank | 4 |

Type | uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Tatoh |

Coxeter diagram | |

Elements | |

Cells | 2N truncated tetrahedra, N cuboctahedra, N truncated octahedra |

Faces | 8N triangles, 6N squares, 8N hexagons |

Edges | 6N+24N |

Vertices | 12N |

Vertex figure | Rectangular pyramid, base edge lengths 1 and √2, side edge lengths √3 |

Measures (edge length 1) | |

Vertex density | |

Dual cell volume | |

Related polytopes | |

Army | Tatoh |

Regiment | Tatoh |

Dual | Rhombic pyramidal honeycomb |

Conjugate | None |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | S_{4} |

Convex | Yes |

The **truncated tetrahedral-octahedral honeycomb**, or **tatoh**, also known as the **cantic cubic honeycomb**, is a convex uniform honeycomb. 1 cuboctahedron, 2 truncated octahedra, and 2 truncated tetrahedra join at each vertex of this honeycomb. As one of its names suggests, it can be formed by truncation of the tetrahedral-octahedral honeycomb, or as an alternated faceting from the small rhombated cubic honeycomb.

## Representations[edit | edit source]

A truncated tetrahedral-octahedral honeycomb has the following Coxeter diagrams:

- (full symmetry)
- (P4 symmetry, as truncated cyclotetrahedral honeycomb)
- (as cantic cubic honeycomb)

## Gallery[edit | edit source]

## External links[edit | edit source]

- Klitzing, Richard. "tatoh".

- Wikipedia Contributors. "Cantic cubic honeycomb".
- Binnendyk, Eric. "Category 2: Truncates" (#16).