# Dodecagonal-octahedral duoprism

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

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Twoct |

Coxeter diagram | x12o o4o3x () |

Elements | |

Tera | 12 octahedral prisms, 8 triangular-dodecagonal duoprisms |

Cells | 96 triangular prisms, 12 octahedra, 12 dodecagonal prisms |

Faces | 96 triangles, 144 squares, 6 dodecagons |

Edges | 72+144 |

Vertices | 72 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Ope–oct–ope: 150° |

Titwadip–twip–titwadip: | |

Titwadip–trip–ope: 90° | |

Central density | 1 |

Number of external pieces | 20 |

Level of complexity | 10 |

Related polytopes | |

Army | Twoct |

Regiment | Twoct |

Dual | Dodecagonal-cubic duotegum |

Conjugate | Dodecagrammic-octahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×I2(12), order 1152 |

Convex | Yes |

Nature | Tame |

The **dodecagonal-octahedral duoprism** or **twoct** is a convex uniform duoprism that consists of 12 octahedral prisms and 8 triangular-dodecagonal duoprisms. Each vertex joins 2 octahedral prisms and 4 triangular-dodecagonal duoprisms.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A dodecahedral-octahedral duoprism has the following Coxeter diagrams:

- x12o o4o3x () (full symmetry)
- x6x o3x3o () (dodecagons as dihexagons)
- x12o o4o3x () (octahedra as tetratetrahedra)
- x6x o3x3o () (dodecagons as dihexagons and octahedra as tetratetrahedra)