# Hexagonal-truncated octahedral duoprism

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Hexagonal-truncated octahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Hatoe |

Coxeter diagram | x6o o4x3x |

Elements | |

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

Cells | 36 cubes, 12+24+48 hexagonal prisms, 6 truncated octahedra |

Faces | 36+72+144 squares, 24+48 hexagons |

Edges | 72+144+144 |

Vertices | 144 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Shiddip–hip–hiddip: |

Tope–toe–tope: 120° | |

Hiddip–hip–hiddip: | |

Shiddip–cube–tope: 90° | |

Hiddip–hip–tope: 90° | |

Central density | 1 |

Number of external pieces | 20 |

Level of complexity | 30 |

Related polytopes | |

Army | Hatoe |

Regiment | Hatoe |

Dual | Hexagonal-tetrakis hexahedral duotegum |

Conjugate | Hexagonal-truncated octahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×G_{2}, order 576 |

Convex | Yes |

Nature | Tame |

The **hexagonal-truncated octahedral duoprism** or **hatoe** is a convex uniform duoprism that consists of 6 truncated octahedral prisms, 8 hexagonal duoprisms, and 6 square-hexagonal duoprisms. Each vertex joins 2 truncated octahedral prisms, 1 square-hexagonal duoprism, and 2 hexagonal duoprisms.

This polyteron can be alternated into a triangular-pyritohedral icosahedral duoantiprism, although it cannot be made uniform.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

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

- x6o o4x3x (full symmetry)
- x6o x3x3x
- x3x o4x3x (hexagons as ditrigons)
- x3x x3x3x

## External links[edit | edit source]

- Klitzing, Richard. "hatoe".