# Hexagonal-truncated cubic duoprism

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Hexagonal-truncated cubic duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Hatic |

Coxeter diagram | x6o x4x3o |

Elements | |

Tera | 8 triangular-hexagonal duoprisms, 6 hexagonal-octagonal duoprisms, 6 truncated cubic prisms |

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

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

Edges | 72+144+144 |

Vertices | 144 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Thiddip–hip–hodip: |

Ticcup–tic–ticcup: 120° | |

Thiddip–trip–ticcup: 90° | |

Hodip–op–ticcup: 90° | |

Hodip–hip–hodip: 90° | |

Central density | 1 |

Number of external pieces | 20 |

Level of complexity | 30 |

Related polytopes | |

Army | Hatic |

Regiment | Hatic |

Dual | Hexagonal-triakis octahedral duotegum |

Conjugate | Hexagonal-quasitruncated hexahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×G_{2}, order 576 |

Convex | Yes |

Nature | Tame |

The **hexagonal-truncated cubic duoprism** or **hatic** is a convex uniform duoprism that consists of 6 truncated cubic prisms, 6 hexagonal-octagonal duoprisms and 8 triangular-hexagonal duoprisms. Each vertex joins 2 truncated cubic prisms, 1 triangular-hexagonal duoprism, and 2 hexagonal-octagonal duoprisms.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

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

- x6o x4x3o (full symmetry)
- x3x x4x3o (hexagons as ditrigons)

## External links[edit | edit source]

- Klitzing, Richard. "hatic".