# Cyclotruncated tetrahedral-octahedral honeycomb

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Cyclotruncated tetrahedral-octahedral honeycomb | |
---|---|

Rank | 4 |

Type | uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Cytatoh (old: Batatoh) |

Coxeter diagram | x3x3o3o3*a () |

Elements | |

Cells | N tetrahedra, N truncated tetrahedra |

Faces | 4N triangles, 2N hexagons |

Edges | 6N |

Vertices | 2N |

Vertex figure | Triangular antiprism, edge lengths 1 (base) and √3 (sides) |

Measures (edge length 1) | |

Vertex density | |

Related polytopes | |

Army | Cytatoh |

Regiment | Cytatoh |

Dual | Triangular antitegmatic honeycomb |

Conjugate | None |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | P_{4}×2 |

Convex | Yes |

The **cyclotruncated tetrahedral-octahedral honeycomb**, also known as the **quarter cubic honeycomb**, is a convex uniform honeycomb. 2 tetrahedra and 6 truncated tetrahedra join at each vertex of this honeycomb. It can be formed by applying two successive alternated faceting to the cubic honeycomb.

## Representations[edit | edit source]

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

- x3x3o3o3*a () (full symmetry)
- x3o3o *b4s () (as single alternated faceting)
- s4o3o4s' () (as double alternated faceting)

## Gallery[edit | edit source]

## External links[edit | edit source]

- Klitzing, Richard. "cytatoh".

- Wikipedia Contributors. "Quarter cubic honeycomb".
- Binnendyk, Eric. "Category 7: Triangular Podiumverts" (#140).