# Hexagonal-truncated tetrahedral duoprism

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Hexagonal-truncated tetrahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Hatut |

Coxeter diagram | x6o x3x3o () |

Elements | |

Tera | 4 triangular-hexagonal duoprisms, 4 hexagonal duoprisms, 6 truncated tetrahedral prisms |

Cells | 24 triangular prisms, 6+12+24 hexagonal prisms, 6 truncated tetrahedra |

Faces | 24 triangles, 36+72 squares, 12+24 hexagons |

Edges | 36+72+72 |

Vertices | 72 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tuttip–tut–tuttip: 120° |

Thiddip-hip-hiddip: | |

Thiddip–trip–tuttip: 90° | |

Hiddip-hip-tuttip: 90° | |

Hiddip–hip–hiddip: | |

Central density | 1 |

Number of external pieces | 14 |

Level of complexity | 30 |

Related polytopes | |

Army | Hatut |

Regiment | Hatut |

Dual | Hexagonal-triakis tetrahedral duotegum |

Conjugate | Hexagonal-truncated tetrahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{3}×G_{2}, order 288 |

Convex | Yes |

Nature | Tame |

The **hexagonal-truncated tetrahedral duoprism** or **hatut** is a convex uniform duoprism that consists of 6 truncated tetrahedral prisms, 4 hexagonal duoprisms, and 4 triangular-hexagonal duoprisms. Each vertex joins 2 truncated tetrahedral prisms, 1 triangular-hexagonal duoprism, and 2 hexagonal duoprisms.

## Vertex coordinates[edit | edit source]

The vertices of a hexagonal-truncated tetrahedral duoprism of edge length 1 are given by all permutations and even sign changes of the last three coordinates of:

- ,
- .

## Representations[edit | edit source]

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

- x6o x3x3o () (full symmetry)
- x3x x3x3o () (hexagons as ditrigons)

## External links[edit | edit source]

- Klitzing, Richard. "hatut".