# Dodecagonal-truncated octahedral duoprism

Dodecagonal-truncated octahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Twatoe |

Coxeter diagram | x12o o4x3x () |

Elements | |

Tera | 6 square-dodecagonal duoprisms, 12 truncated octahedral prisms, 8 hexagonal-dodecagonal duoprisms |

Cells | 72 cubes, 96 hexagonal prisms, 12+24 dodecagonal prisms, 12 truncated octahedra |

Faces | 72+144+288 squares, 96 hexagons, 24 dodecagons |

Edges | 144+288+288 |

Vertices | 288 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tope–toe–tope: 150° |

Sitwadip–twip–hitwadip: | |

Hitwadip–twip–hitwadip: | |

Sitwadip–cube–tope: 90° | |

Hitwadip–hip–tope: 90° | |

Central density | 1 |

Number of external pieces | 26 |

Level of complexity | 30 |

Related polytopes | |

Army | Twatoe |

Regiment | Twatoe |

Dual | Dodecagonal-tetrakis hexahedral duotegum |

Conjugate | Dodecagrammic-truncated octahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×I_{2}(12), order 1152 |

Convex | Yes |

Nature | Tame |

The **dodecagonal-truncated octahedral duoprism** or **twatoe** is a convex uniform duoprism that consists of 12 truncated octahedral prisms, 8 hexagonal-dodecagonal duoprisms, and 6 square-dodecagonal duoprisms. Each vertex joins 2 truncated octahedral prisms, 1 square-dodecagonal duoprism, and 2 hexagonal-dodecagonal duoprisms.

This polyteron can be alternated into a hexagonal-pyritohedral icosahedral duoantiprism, although it cannot be made uniform. The dodecagons can also be alternated into long ditrigons to create a pyritohedral icosahedral-hexagonal prismantiprismoid, which is also nonuniform.

## Vertex coordinates[edit | edit source]

The vertices of a dodecagonal-truncated octahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of:

## Representations[edit | edit source]

A dodecagonal-truncated octahedral duoprism has the following Coxeter diagrams:

- x12o o4x3x () (full symmetry)
- x12o x3x3x ()
- x6x o4x3x () (dodecagons as dihexagons)
- x6x x3x3x ()