# Hexagonal duoprismatic prism

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

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Hahip |

Coxeter diagram | x x6o x6o () |

Elements | |

Tera | 12 square-hexagonal duoprisms, 2 hexagonal duoprisms |

Cells | 36 cubes, 12+24 hexagonal prisms |

Faces | 72+72 squares, 24 hexagons |

Edges | 36+144 |

Vertices | 72 |

Vertex figure | Tetragonal disphenoidal pyramid, edge lengths √3 (disphenoid bases) and √2 (remaining edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Shiddip–hip–shiddip: 120° |

Shiddip–cube–shiddip: 90° | |

Hiddip–hip–shiddip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 14 |

Level of complexity | 15 |

Related polytopes | |

Army | Hahip |

Regiment | Hahip |

Dual | Hexagonal duotegmatic tegum |

Conjugate | Hexagonal duoprismatic prism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | G_{2}≀S_{2}×A_{1}, order 576 |

Convex | Yes |

Nature | Tame |

The **hexagonal duoprismatic prism** or **hahip**, also known as the **hexagonal-hexagonal prismatic duoprism**, is a convex uniform duoprism that consists of 2 hexagonal duoprisms and 12 square-hexagonal duoprisms. Each vertex joins 4 square-hexagonal duoprisms and 1 hexagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

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

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A hexagonal duoprismatic prism has the following Coxeter diagrams:

- x x6o x6o (full symmetry)
- x x3x x3x () (hexagons as ditrigons)
- xx6oo xx6oo&#x (hexagonal duoprism atop hexagonal duoprism)
- xx3xx xx3xx&#x

## External links[edit | edit source]

- Klitzing, Richard. "hahip".