# Octagonal-dodecahedral duoprism

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Octagonal-dodecahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Odoe |

Coxeter diagram | x8o x5o3o |

Elements | |

Tera | 12 pentagonal-octagonal duoprisms, 8 dodecahedral prisms |

Cells | 96 pentagonal prisms, 30 octagonal prisms, 8 dodecahedra |

Faces | 240 squares, 96 pentagons, 20 octagons |

Edges | 160+240 |

Vertices | 160 |

Vertex figure | Triangular scalene, edge lengths (1+√5)/2 (base triangle), √2+√2 (top), √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Dope–doe–dope: 135° |

Podip–op–podip: | |

Podip–pip–dope: 90° | |

Central density | 1 |

Number of external pieces | 20 |

Level of complexity | 10 |

Related polytopes | |

Army | Odoe |

Regiment | Odoe |

Dual | Octagonal-icosahedral duotegum |

Conjugates | Octagrammic-dodecahedral duoprism, Octagonal-great stellated dodecahedral duoprism, Octagrammic-great stellated dodecahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×I2(8), order 1920 |

Convex | Yes |

Nature | Tame |

The **octagonal-dodecahedral duoprism** or **odoe** is a convex uniform duoprism that consists of 8 dodecahedral prisms and 12 pentagonal-octagonal duoprisms. Each vertex joins 2 dodecahedral prisms and 3 pentagonal-octagonal duoprisms.

## Vertex coordinates[edit | edit source]

The vertices of an octagonal-dodecahedral duoprism of edge length 1 are given by:

as well as all even permutations of the last three coordinates of:

## Representations[edit | edit source]

An octagonal-dodecahedral duoprism has the following Coxeter diagrams:

- x8o x5o3o (full symmetry)
- x4x x5o3o (octagons as ditetragons)

## External links[edit | edit source]

- Klitzing, Richard. "odoe".