# Heptagonal-square antiprismatic duoprism

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Heptagonal-square antiprismatic duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Hesquap |

Coxeter diagram | x7o s2s8o |

Elements | |

Tera | 7 square antiprismatic prisms, 8 triangular-heptagonal duoprisms, 2 square-heptagonal duoprisms |

Cells | 56 triangular prisms, 14 cubes, 7 square antiprisms, 8+8 heptagonal prisms |

Faces | 56 triangles, 14+56+56 squares, 8 heptagons |

Edges | 56+56+56 |

Vertices | 56 |

Vertex figure | Isosceles-trapezoidal scalene, edge lengths 1, 1, 1, √2 (base trapezoid), 2cos(π/7) (top), √2 (side edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Squappip–squap–squappip: |

Theddip–hep–theddip: = | |

Theddip–hep–squahedip: = | |

Theddip–trip–squappip: 90° | |

Squahedip–cube–squappip: 90° | |

Central density | 1 |

Number of external pieces | 17 |

Level of complexity | 40 |

Related polytopes | |

Army | Hesquap |

Regiment | Hesquap |

Dual | Heptagonal-square antitegmatic duotegum |

Conjugates | Heptagrammic-square antiprismatic duoprism, Great heptagrammic-square antiprismatic duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(7)×I_{2}(8)×A_{1}+, order 224 |

Convex | Yes |

Nature | Tame |

The **heptagonal-square antiprismatic duoprism** or **hesquap** is a convex uniform duoprism that consists of 7 square antiprismatic prisms, 2 square-heptagonal duoprisms, and 8 triangular-heptagonal duoprisms. Each vertex joins 2 square antiprismatic prisms, 3 triangular-heptagonal duoprisms, and 1 square-heptagonal duoprism.

## Vertex coordinates[edit | edit source]

The vertices of a heptagonal-square antiprismatic duoprism of edge length 2sin(π/7) are given by:

where j = 2, 4, 6.

## Representations[edit | edit source]

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

- x7o s2s8o (full symmetry; square antiprisms as alternated octagonal prisms)
- x7o s2s4s (square antiprisms as alternated ditetragonal prisms)