# Triangular-truncated tetrahedral duoprism

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Triangular-truncated tetrahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Tratut |

Coxeter diagram | x3o x3x3o () |

Elements | |

Tera | 4 triangular duoprisms, 4 triangular-hexagonal duoprisms, 3 truncated tetrahedral prisms |

Cells | 6+12+12 triangular prisms, 12 hexagonal prisms, 3 truncated tetrahedra |

Faces | 12+12 triangles, 18+36 squares, 12 hexagons |

Edges | 18+36+36 |

Vertices | 36 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Triddip–trip–thiddip: |

Triddip–trip–tuttip: 90° | |

Thiddip–hip–tuttip: 90° | |

Thiddip–trip–thiddip: | |

Tuttip–tut–tuttip: 60° | |

Height | |

Central density | 1 |

Number of external pieces | 11 |

Level of complexity | 30 |

Related polytopes | |

Army | Tratut |

Regiment | Tratut |

Dual | Triangular-triakis tetrahedral duotegum |

Conjugate | None |

Abstract & topological properties | |

Flag count | 4320 |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{3}×A_{2}, order 144 |

Convex | Yes |

Nature | Tame |

The **triangular-truncated tetrahedral duoprism** or **tratut** is a convex uniform duoprism that consists of 3 truncated tetrahedral prisms, 4 triangular-hexagonal duoprisms, and 4 triangular duoprisms. Each vertex joins 2 truncated tetrahedral prisms, 1 triangular duoprism, and 2 triangular-hexagonal duoprisms. It is a duoprism based on a triangle and a truncated tetrahedron, which makes it a convex segmentoteron.

## Vertex coordinates[edit | edit source]

The vertices of a triangular-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 triangular-truncated tetrahedral duoprism has the following Coxeter diagrams:

- x3o x3x3o () (full symmetry)
- ox oo3xx3xx&#x (tut atop tuttip)
- ooo3xxx3xxx&#x

## External links[edit | edit source]

- Klitzing, Richard. "tratut".

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