# Octagonal-octahedral duoprism

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Octagonal-octahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Owoct |

Coxeter diagram | x8o o4o3x () |

Elements | |

Tera | 8 octahedral prisms, 8 triangular-octagonal duoprisms |

Cells | 64 triangular prisms, 8 octahedra, 12 octagonal prisms |

Faces | 64 triangles, 96 squares, 6 octagons |

Edges | 48+96 |

Vertices | 48 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Ope–oct–ope: 135° |

Todip–op–todip: | |

Todip–trip–ope: 90° | |

Central density | 1 |

Number of external pieces | 16 |

Level of complexity | 10 |

Related polytopes | |

Army | Owoct |

Regiment | Owoct |

Dual | Octagonal-cubic duotegum |

Conjugate | Octagrammic-octahedral duoprism |

Abstract & topological properties | |

Flag count | 7680 |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×I_{2}(8), order 768 |

Convex | Yes |

Nature | Tame |

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

## Vertex coordinates[edit | edit source]

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

- ,
- .

## Representations[edit | edit source]

An octagonal-octahedral duoprism has the following Coxeter diagrams:

- x8o o4o3x () (full symmetry)
- x4x o4o3x () (octagons as ditetragons)
- x8o o3x3o () (octahedra as tetratetrahedra)
- x4x o3x3o () (octagons as ditetragons and octahedra as tetratetrahedra)
- xo3ox xx8oo&#x (triangular-octagonal duoprism atop triangle-gyrated triangular-octagonal duoprism)

## External links[edit | edit source]

- Klitzing, Richard. "owoct".