# Hexagonal-square antiprismatic duoprism

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Hexagonal-square antiprismatic duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Hasquap |

Coxeter diagram | x6o s2s8o |

Elements | |

Tera | 6 square antiprismatic prisms, 8 triangular-hexagonal duoprisms, 2 square-hexagonal duoprisms |

Cells | 48 triangular prisms, 12 cubes, 6 square antiprisms, 8+8 hexagonal prisms |

Faces | 48 triangles, 12+48+48 squares, 8 hexagons |

Edges | 48+48+48 |

Vertices | 48 |

Vertex figure | Isosceles-trapezoidal scalene, edge lengths 1, 1, 1, √2 (base trapezoid), √3 (top), √2 (side edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Thiddip–hip–thiddip: |

Squappip–squap–squappip: 120° | |

Thiddip–hip–shiddip: = | |

Thiddip–trip–squappip: 90° | |

Shiddip–cube–squappip: 90° | |

Central density | 1 |

Number of external pieces | 16 |

Level of complexity | 40 |

Related polytopes | |

Army | Hasquap |

Regiment | Hasquap |

Dual | Hexagonal-square antitegmatic duotegum |

Conjugate | Hexagonal-square antiprismatic duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | G_{2}×I_{2}(8)×A_{1}+, order 192 |

Convex | Yes |

Nature | Tame |

The **hexagonal-square antiprismatic duoprism** or **hasquap** is a convex uniform duoprism that consists of 6 square antiprismatic prisms, 2 square-hexagonal duoprisms, and 8 triangular-hexagonal duoprisms. Each vertex joins 2 square antiprismatic prisms, 3 triangular-hexagonal duoprisms, and 1 square-hexagonal duoprism.

## Vertex coordinates[edit | edit source]

The vertices of a hexagonal-square antiprismatic duoprism of edge length 1 are given by:

## Representations[edit | edit source]

A hexagonal-square antiprismatic duoprism has the following Coxeter diagrams:

- x6o s2s8o (full symmetry; square antiprisms as alternated octagonal prisms)
- x6o s2s4s (square antiprisms as alternated ditetragonal prisms)
- x3x s2s8o (hexagons as ditrigons)
- x3x s2s4s