# Hexagonal-tetrahedral duoprism

Jump to navigation
Jump to search

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

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Hatet |

Coxeter diagram | x6o x3o3o () |

Elements | |

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

Cells | 6 tetrahedra, 24 triangular prisms, 6 hexagonal prisms |

Faces | 24 triangles, 36 squares, 4 hexagons |

Edges | 24+36 |

Vertices | 24 |

Vertex figure | Triangular scalene, edge lengths 1 (base triangle), √3 (top), √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tepe–tet–tepe: 120° |

Tepe–trip–thiddip: 90° | |

Thiddip–hip–thiddip: | |

Heights | Hig atop thiddip: |

Hip atop perp hip: | |

Central density | 1 |

Number of external pieces | 10 |

Level of complexity | 10 |

Related polytopes | |

Army | Hatet |

Regiment | Hatet |

Dual | Hexagonal-tetrahedral duotegum |

Conjugate | None |

Abstract & topological properties | |

Flag count | 2880 |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{3}×G_{2}, order 288 |

Convex | Yes |

Nature | Tame |

The **hexagonal-tetrahedral duoprism** or **hatet** is a convex uniform duoprism that consists of 6 tetrahedral prisms and 4 triangular-hexagonal duoprisms. Each vertex joins 2 tetrahedral prisms and 3 triangular-hexagonal duoprisms.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A hexagonal-tetrahedral duoprism has the following Coxeter diagrams:

- x6o x3o3o (full symmetry)
- x3x x3o3o (hexagons as ditrigons)
- ox3oo xx6oo&#x (hexagon atop triangular-hexagonal duoprism)
- ox3oo xx3xx&#x
- ox xo xx6oo&#x (hexagonal prism atop orthogonal hexagonal prism)
- ox xo xx3xx&#x
- oox xxx3xxx&#x
- xxxx3xxxx&#x

## External links[edit | edit source]

- Klitzing, Richard. "hatet".