# Decagonal-truncated octahedral duoprism

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

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Datoe |

Coxeter diagram | x10o o4x3x () |

Elements | |

Tera | 6 square-decagonal duoprisms, 10 truncated octahedral prisms, 8 hexagonal-decagonal duoprisms |

Cells | 60 cubes, 80 hexagonal prisms, 12+24 decagonal prisms, 10 truncated octahedra |

Faces | 60+120+240 squares, 80 hexagons, 24 decagons |

Edges | 120+240+240 |

Vertices | 240 |

Vertex figure | Digonal disphenoidal pyramid, edge lengths √2, √3, √3 (base triangle), √(5+√5)/2 (top), √2 (side edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tope–toe–tope: 144° |

Squadedip–dip–hadedip: | |

Hadedip–dip–hadedip: | |

Squadedip–cube–tope: 90° | |

Hadedip–hip–tope: 90° | |

Central density | 1 |

Number of external pieces | 24 |

Level of complexity | 30 |

Related polytopes | |

Army | Datoe |

Regiment | Datoe |

Dual | Decagonal-tetrakis hexahedral duotegum |

Conjugate | Decagrammic-truncated octahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×I2(10), order 960 |

Convex | Yes |

Nature | Tame |

The **decagonal-truncated octahedral duoprism** or **datoe** is a convex uniform duoprism that consists of 10 truncated octahedral prisms, 8 hexagonal-decagonal duoprisms, and 6 square-decagonal duoprisms. Each vertex joins 2 truncated octahedral prisms, 1 square-decagonal duoprism, and 2 hexagonal-decagonal duoprisms.

This polyteron can be alternated into a pentagonal-pyritohedral icosahedral duoantiprism, although it cannot be made uniform.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A decagonal-truncated octahedral duoprism has the following Coxeter diagrams:

- x10o o4x3x (full symmetry)
- x10o x3x3x
- x5x o4x3x (decagons as dipentagons)
- x5x x3x3x