# Gyrated tetrahedral-octahedral honeycomb

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Gyrated tetrahedral-octahedral honeycomb | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Gytoh |

Coxeter diagram | |

Elements | |

Cells | 2N tetrahedra, N octahedra |

Faces | N+N+6N triangles |

Edges | 3N+3N |

Vertices | N |

Vertex figure | Triangular orthobicupola, edge length 1 |

Related polytopes | |

Army | Gytoh |

Regiment | Gytoh |

Dual | Rhombitrapezohedral dodecahedral honeycomb |

Conjugate | None |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | V_{3}❘W_{2} |

Convex | Yes |

The **gyrated tetrahedral-octahedral honeycomb**, also known as the **gyrated alternated cubic honeycomb**, is a convex uniform honeycomb. 6 octahedra and 8 tetrahedra join at each vertex of this honeycomb. It is also the alternated hexagonal prismatic honeycomb.

This honeycomb can be formed from the tetrahedral-octahedral honeycomb by gyrating alternate layers of cells, so that some tetrahedra join to other tetrahedra, and some octahedra connect to other octahedra. In the normal tetrahedral-octahedral honeycomb, triangles always join one tetrahedron and one octahedron. As a result, the tetrahedral-octahedral honeycomb's cuboctahedral vertex figure turns into a triangular orthobicupola, or gyrated cuboctahedron.

## Gallery[edit | edit source]

## External links[edit | edit source]

- Klitzing, Richard. "gytoh".

- Wikipedia Contributors. "Gyrated tetrahedral-octahedral honeycomb".