# Small rhombi-tetrahedral-octahedral honeycomb

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Small rhombi-tetrahedral-octahedral honeycomb | |
---|---|

Rank | 4 |

Type | uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Sratoh |

Coxeter diagram | x3o3o *b4x () |

Elements | |

Cells | 2N tetrahedra, N cubes, N small rhombicuboctahedra |

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

Edges | 12N+12N |

Vertices | 8N |

Vertex figure | Triangular frustum, edge lengths 1 (top) and √2 (sides and base) |

Measures (edge length 1) | |

Vertex density | |

Dual cell volume | |

Related polytopes | |

Army | Sratoh |

Regiment | Sratoh |

Dual | Apiculated triangular pyramidal honeycomb |

Conjugate | Quasirhombi-tetrahedral-octahedral honeycomb |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | S_{4} |

Convex | Yes |

The **small rhombi-tetrahedral-octahedral honeycomb**, or **sratoh**, also known as the **runcic cubic honeycomb**, is a convex uniform honeycomb. 1 tetrahedron, 1 cube, and 3 small rhombicuboctahedra join at each vertex of this honeycomb. It can be formed as an alternated faceting from the cubic honeycomb, alternating a subset of the cubes, or alternately as the birectification of the tetrahedral-octahedral honeycomb.

It can be subdivided into alternating truncated square tiling prism and truncated square tiling alterprism segments.

## Representations[edit | edit source]

A small rhombated tetrahedral-octahedral honeycomb has the following Coxeter diagrams:

- x3o3o *b4x (full symmetry)
- s4o3o4x (as runcic cubic honeycomb)
- qo3xx3oq3oo&#zx

## Gallery[edit | edit source]

## External links[edit | edit source]

- Klitzing, Richard. "sratoh".

- Wikipedia Contributors. "Runcic cubic honeycomb".
- Binnendyk, Eric. "Category 7: Triangular Podiumverts" (#152).