# Hexagonal-decagonal duoprismatic prism

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Hexagonal-decagonal duoprismatic prism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Hadip |

Coxeter diagram | x x6o x10o |

Elements | |

Tera | 10 square-hexagonal duoprisms, 6 square-decagonal duoprisms, 2 hexagonal-decagonal duoprisms |

Cells | 60 cubes, 6+12 decagonal prisms, 10+20 hexagonal prisms |

Faces | 60+60+120 squares, 20 hexagons, 12 decagons |

Edges | 60+120+120 |

Vertices | 120 |

Vertex figure | Digonal disphenoidal pyramid, edge lengths √3 (disphenoid base 1), √(5+√5)/2 (disphenoid base 2), √2 (remaining edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Shiddip–hip–shiddip: 144° |

Squadedip–dip–squadedip: 120° | |

Squadedip–cube–shiddip: 90° | |

Hadedip–hip–shiddip: 90° | |

Squadedip–dip–hadedip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 18 |

Level of complexity | 30 |

Related polytopes | |

Army | Hadip |

Regiment | Hadip |

Dual | Hexagonal-decagonal duotegmatic tegum |

Conjugate | Hexagonal-decagrammic duoprismatic prism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | G_{2}×I_{2}(10)×A_{1}, order 480 |

Convex | Yes |

Nature | Tame |

The **hexagonal-decagonal duoprismatic prism** or **hadip**, also known as the **hexagonal-decagonal prismatic duoprism**, is a convex uniform duoprism that consists of 2 hexagonal-decagonal duoprisms, 6 square-decagonal duoprisms, and 10 square-hexagonal duoprisms. Each vertex joins 2 square-hexagonal duoprisms, 2 square-decagonal duoprisms, and 1 hexagonal-decagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

This polyteron can be alternated into a triangular-pentagonal duoantiprismatic antiprism, although it cannot be made uniform.

## Vertex coordinates[edit | edit source]

The vertices of a hexagonal-decagonal duoprismatic prism of edge length 1 are given by:

## Representations[edit | edit source]

A hexagonal-decagonal duoprismatic prism has the following Coxeter diagrams:

- x x6o x10o (full symmetry)
- x x3x x10o (hexagons as ditrigons)
- x x6o x5x (decagons as dipentagons)
- x x3x x5x
- xx6oo xx10oo&#x (hexagonal-decagonal duoprism atop hexagonal-decagonal duoprism)
- xx3xx xx10oo&#x
- xx6oo xx5xx&#x
- xx3xx xx5xx&#x