# Decagonal-octahedral duoprism

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Decagonal-octahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Doct |

Coxeter diagram | x10o o4o3x () |

Elements | |

Tera | 10 octahedral prisms, 8 triangular-decagonal duoprisms |

Cells | 80 triangular prisms, 10 octahedra, 12 decagonal prisms |

Faces | 80 triangles, 120 squares, 6 decagons |

Edges | 60+120 |

Vertices | 60 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Ope–oct–ope: 144° |

Tradedip–dip–tradedip: | |

Tradedip–trip–ope: 90° | |

Height | |

Central density | 1 |

Number of external pieces | =18 |

Level of complexity | 10 |

Related polytopes | |

Army | Doct |

Regiment | Doct |

Dual | Decagonal-cubic duotegum |

Conjugate | Decagrammic-octahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×I2(10), order 960 |

Convex | Yes |

Nature | Tame |

The **decagonal-octahedral duoprism** or **doct** is a convex uniform duoprism that consists of 10 octahedral prisms and 8 triangular-decagonal duoprisms. Each vertex joins 2 octahedral prisms and 4 triangular-decagonal duoprisms.

## Vertex coordinates[edit | edit source]

The vertices of a decagonal-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 triangular-octahedral duoprism has the following Coxeter diagrams:

- x10o o4o3x (full symmetry)
- x5x o4o3x (decagons as dipentagons)
- x10o o3x3o (octahedra as tetratetrahedra)
- x5x o3x3o (decagons as dipentagons and octahedra as tetratetrahedra)