# Octagonal-cuboctahedral duoprism

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Octagonal-cuboctahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Oco |

Coxeter diagram | x8o o4x3o |

Elements | |

Tera | 8 cuboctahedral prisms, 8 triangular-octagonal duoprisms, 6 square-octagonal duoprisms |

Cells | 64 triangular prisms, 48 cubes, 8 cuboctahedra, 24 octagonal prisms |

Faces | 64 triangles, 48+192 squares, 12 octagons |

Edges | 96+192 |

Vertices | 96 |

Vertex figure | Rectangular scalene, edge lengths 1, √2, 1, √2 (base rectangle), √2+√2 (top), √2 (side edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Cope–co–cope: 135° |

Todip–op–sodip: | |

Todip–trip–cope: 90° | |

Sodip–cube–cope: 90° | |

Central density | 1 |

Number of external pieces | 22 |

Level of complexity | 20 |

Related polytopes | |

Army | Oco |

Regiment | Oco |

Dual | Octagonal-rhombic dodecahedral duotegum |

Conjugate | Octagrammic-cuboctahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×I2(8), order 768 |

Convex | Yes |

Nature | Tame |

The **octagonal-cuboctahedral duoprism** or **oco** is a convex uniform duoprism that consists of 8 cuboctahedral prisms, 6 square-octagonal duoprisms, and 8 triangular-octagonal duoprisms. Each vertex joins 2 cuboctahedral prisms, 2 triangular-octagonal duoprisms, and 2 square-octagonal duoprisms.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

An octagonal-cuboctahedral duoprism has the following Coxeter diagrams:

- x8o o4x3o (full symmetry)
- x4x o4x3o (octagons as ditetragons)
- x8o x3o3x
- x4x x3o3x

## External links[edit | edit source]

- Klitzing, Richard. "oco".