# Elongated tetrahedral-octahedral honeycomb

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Elongated tetrahedral-octahedral honeycomb | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Etoh |

Elements | |

Cells | 2N tetrahedra, N octahedra, 2N triangular prisms |

Faces | 2N+2N+6N triangles, 3N squares |

Edges | N+3N+6N |

Vertices | 2N |

Vertex figure | Hexakis triangular cupola, edge lengths 1 (cupola part) and √2 (sides of augment) |

Related polytopes | |

Army | Etoh |

Regiment | Etoh |

Conjugate | Retroelongated tetrahedral-octahedral honeycomb |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | V_{3}❘W_{2}+ |

Convex | Yes |

Nature | Tame |

The **elongated tetrahedral-octahedral honeycomb**, or **etoh**, also known as the **elongated alternated cubic honeycomb**, is a convex uniform honeycomb. 3 octahedra, 4 tetrahedra, and 6 triangular prisms join at each vertex of this honeycomb.

It can be formed by inserting layers of triangular prisms between layers of cells of the tetrahedral-octahedral honeycomb. It shares its vertex figure with the gyroelongated tetrahedral-octahedral honeycomb.

## External links[edit | edit source]

- Klitzing, Richard. "etoh".
- Wikipedia contributors. "Elongated alternated cubic honeycomb".