# Decagonal-cubic duoprism

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Decagonal-cubic duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Dacube |

Coxeter diagram | x10o x4o3o () |

Elements | |

Tera | 10 tesseracts, 6 square-decagonal duoprisms |

Cells | 10+60 cubes, 12 decagonal prisms |

Faces | 60+120 squares, 8 decagons |

Edges | 80+120 |

Vertices | 80 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tes–cube–tes: 144° |

Tes–cube–squadedip: 90° | |

Squadedip–dip–squadedip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 16 |

Level of complexity | 10 |

Related polytopes | |

Army | Dacube |

Regiment | Dacube |

Dual | Decagonal-octahedral duotegum |

Conjugate | Decagrammic-cubic duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×I2(10), order 960 |

Convex | Yes |

Nature | Tame |

The **decagonal-cubic duoprism** or **dacube**, also known as the **square-decagonal duoprismatic prism**, is a convex uniform duoprism that consists of 10 tesseracts and 6 square-decagonal duoprisms. Each vertex joins 2 tesseracts and 3 square-decagonal duoprisms. It is a duoprism based on a square and a decagonal prism, which makes it a convex segmentoteron.

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

## Vertex coordinates[edit | edit source]

The vertices of a decagonal-cubic duoprism of edge length 1 are given by:

## Representations[edit | edit source]

A decagonal-cubic duoprism has the following Coxeter diagrams:

- x10o x4o3o () (full symmetry)
- x x4o x10o () (square-decagonal duoprismatic prism)
- x x x x10o () (decagonal prismatic prismatic prism)