# Octagonal-truncated octahedral duoprism

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

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Otoe |

Coxeter diagram | x8o o4x3x () |

Elements | |

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

Cells | 48 cubes, 64 hexagonal prisms, 12+24 octagonal prisms, 8 truncated octahedra |

Faces | 48+96+192 squares, 64 hexagons, 24 octagons |

Edges | 96+192+192 |

Vertices | 192 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tope–toe–tope: 135° |

Sodip–op–hodip: | |

Hodip–op–hodip: | |

Sodip–cube–tope: 90° | |

Hodip–hip–tope: 90° | |

Central density | 1 |

Number of external pieces | 22 |

Level of complexity | 30 |

Related polytopes | |

Army | Otoe |

Regiment | Otoe |

Dual | Octagonal-tetrakis hexahedral duotegum |

Conjugate | Octagrammic-truncated octahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

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

Convex | Yes |

Nature | Tame |

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

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

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

An octagonal-truncated octahedral duoprism has the following Coxeter diagrams:

- x8o o4x3x (full symmetry)
- x8o x3x3x ()
- x4x o4x3x () (octagons as ditetragons)
- x4x x3x3x ()

## External links[edit | edit source]

- Klitzing, Richard. "otoe".