# Triangular-truncated octahedral duoprism

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Triangular-truncated octahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Tratoe |

Coxeter diagram | x3o o4x3x () |

Elements | |

Tera | 6 triangular-square duoprisms, 8 triangular-hexagonal duoprisms, 3 truncated octahedral prisms |

Cells | 12+24 triangular prisms, 18 cubes, 24 hexagonal prisms, 3 truncated octahedra |

Faces | 24 triangles, 18+36+72 squares, 24 hexagons |

Edges | 36+72+72 |

Vertices | 72 |

Vertex figure | Digonal disphenoidal pyramid, edge lengths √2, √3, √3 (base triangle), 1 (top), √2 (side edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tisdip–trip–thiddip: |

Thiddip–trip–thiddip: | |

Tisdip–cube–tope: 90° | |

Thiddip–hip–tope: 90° | |

Tope–toe–tope: 60° | |

Height | |

Central density | 1 |

Number of external pieces | 17 |

Level of complexity | 30 |

Related polytopes | |

Army | Tratoe |

Regiment | Tratoe |

Dual | Triangular-tetrakis hexahedral duotegum |

Conjugate | None |

Abstract & topological properties | |

Flag count | 8640 |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×A_{2}, order 288 |

Convex | Yes |

Nature | Tame |

The **triangular-truncated octahedral duoprism** or **tratoe** is a convex uniform duoprism that consists of 3 truncated octahedral prisms, 8 triangular-hexagonal duoprisms, and 6 triangular-square duoprisms. Each vertex joins 2 truncated octahedral prisms, 1 triangular-square duoprism, and 2 triangular-hexagonal duoprisms. It is a duoprism based on a triangle and a truncated octahedron, which makes it a convex segmentoteron.

## Vertex coordinates[edit | edit source]

The vertices of a triangular-truncated octahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of:

## Representations[edit | edit source]

A triangular-truncated octahedral duoprism has the following Coxeter diagrams:

- x3o o4x3x (full symmetry)
- x3o x3x3x
- ox xx3xx3xx&#x (truncated octahedron atop truncated octahedral prism)
- xxx3xxx3xxx&#x

## External links[edit | edit source]

- Klitzing, Richard. "tratoe".