# Dodecagonal-tetrahedral duoprism

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Dodecagonal-tetrahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Twatet |

Coxeter diagram | x12o x3o3o () |

Elements | |

Tera | 12 tetrahedral prisms, 4 triangular-dodecagonal duoprisms |

Cells | 12 tetrahedra, 48 triangular prisms, 6 dodecagonal prisms |

Faces | 48 triangles, 72 squares, 4 dodecagons |

Edges | 48+72 |

Vertices | 48 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tepe–tet–tepe: 150° |

Tepe–trip–titwadip: 90° | |

Titwadip–twip–titwadip: | |

Heights | Dog atop titwadip: |

Twip atop perp twip: | |

Central density | 1 |

Number of external pieces | 16 |

Level of complexity | 10 |

Related polytopes | |

Army | Twatet |

Regiment | Twatet |

Dual | Dodecagonal-tetrahedral duotegum |

Conjugate | Dodecagrammic-tetrahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{3}×I2(12), order 576 |

Convex | Yes |

Nature | Tame |

The **dodecagonal-tetrahedral duoprism** or **twatet** is a convex uniform duoprism that consists of 12 tetrahedral prisms and 4 triangular-dodecagonal duoprisms. Each vertex joins 2 tetrahedral prisms and 3 triangular-dodecagonal duoprisms.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A dodecagonal-tetrahedral duoprism has the following Coxeter diagrams:

- x12o x3o3o () (full symmetry)
- x6x x3o3o () (dodecagons as dihexagons)