# Decagonal-cuboctahedral duoprism

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Decagonal-cuboctahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Daco |

Coxeter diagram | x10o o4x3o () |

Elements | |

Tera | 10 cuboctahedral prisms, 8 triangular-decagonal duoprisms, 6 square-decagonal duoprisms |

Cells | 80 triangular prisms, 60 cubes, 10 cuboctahedra, 24 decagonal prisms |

Faces | 80 triangles, 60+240 squares, 12 decagons |

Edges | 120+240 |

Vertices | 120 |

Vertex figure | Rectangular scalene, edge lengths 1, √2, 1, √2 (base rectangle), √(5+√5)/2 (top), √2 (side edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Cope–co–cope: 144° |

Tradedip–dip–squadedip: | |

Tradedip–trip–cope: 90° | |

Squadedip–cube–cope: 90° | |

Central density | 1 |

Number of external pieces | 24 |

Level of complexity | 20 |

Related polytopes | |

Army | Daco |

Regiment | Daco |

Dual | Decagonal-rhombic dodecahedral duotegum |

Conjugate | Decagrammic-cuboctahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×I2(10), order 960 |

Convex | Yes |

Nature | Tame |

The **decagonal-cuboctahedral duoprism** or **daco** is a convex uniform duoprism that consists of 10 cuboctahedral prisms, 6 square-decagonal duoprisms, and 8 triangular-decagonal duoprisms. Each vertex joins 2 cuboctahedral prisms, 2 triangular-decagonal duoprisms, and 2 square-decagonal duoprisms.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A decagonal-cuboctahedral duoprism has the following Coxeter diagrams:

- x10o o4x3o () (full symmetry)
- x5o o4x3o () (decagons as dipentagons)
- x10o x3o3x ()
- x5x x3o3x ()