# Triangular-tetrahedral duoprism

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

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Tratet |

Coxeter diagram | x3o x3o3o () |

Tapertopic notation | 1^{2}1^{1} |

Elements | |

Tera | 3 tetrahedral prisms, 4 triangular duoprisms |

Cells | 3 tetrahedra, 6+12 triangular prisms |

Faces | 4+12 triangles, 18 squares |

Edges | 12+18 |

Vertices | 12 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tepe–trip–triddip: 90° |

triddip–trip–triddip: | |

Tepe–tet–tepe: 60° | |

Heights | Tet atop tepe: |

Trig atop triddip: | |

Trip atop perp trip: | |

Central density | 1 |

Number of external pieces | 7 |

Level of complexity | 10 |

Related polytopes | |

Army | Tratet |

Regiment | Tratet |

Dual | Triangular-tetrahedral duotegum |

Conjugate | None |

Abstract & topological properties | |

Flag count | 1440 |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{3}×A_{2}, order 144 |

Flag orbits | 10 |

Convex | Yes |

Nature | Tame |

The **triangular-tetrahedral duoprism** or **tratet** is a convex uniform duoprism that consists of 3 tetrahedral prisms and 4 triangular duoprisms. Each vertex joins 2 tetrahedral prisms and 3 triangular duoprisms. It is a duoprism based on a triangle and a tetrahedron, and is thus also a convex segmentoteron, as a tetrahedron atop tetrahedral prism.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A triangular-tetrahedral duoprism has the following Coxeter diagrams:

- x3o x3o3o (full symmetry)
- xx3oo ox3oo&#x (A2×A2 symmetry, triangle atop triangular duoprism)
- ox xx3oo3oo&#x (A3×A1 symmetry, tetrahedron atop tetrahedral prism)
- ox xo xx3oo&#x (A2×A1×A1 symmetry, triangular prism atop orthogonal triangular prism)
- ooo3ooo3xxx&#x (A3 symmetry, tetrahedra considered different)
- oox ooo3xxx&#x (A2×A1 symmetry, tetrahedra have mirror symmetry only)
- oooo3xxxx&#x (A2 symmetry, tetrahedra have no symmetry)
- xxoo xoox3oooo&#xr (A2×A1 symmetry)

## External links[edit | edit source]

- Klitzing, Richard. "tratet".