# Octagonal-hexagonal antiprismatic duoprism

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Octagonal-hexagonal antiprismatic duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Ohap |

Coxeter diagram | x8o s2s12o |

Elements | |

Tera | 8 hexagonal antiprismatic prisms, 12 triangular-octagonal duoprisms, 2 hexagonal-octagonal duoprisms |

Cells | 96 triangular prisms, 16 hexagonal prisms, 8 hexagonal antiprisms, 12+12 octagonal prisms |

Faces | 96 triangles, 96+96 squares, 16 hexagons, 12 octagons |

Edges | 96+96+96 |

Vertices | 96 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Todip–op–todip: = |

Happip–hap–happip: 135° | |

Todip–op–hodip: = | |

Todip–trip–happip: 90° | |

Hodip–hip–happip: 90° | |

Height | |

Central density | 1 |

Number of external pieces | 22 |

Level of complexity | 40 |

Related polytopes | |

Army | Ohap |

Regiment | Ohap |

Dual | Octagonal-hexagonal antitegmatic duotegum |

Conjugate | Octagrammic-hexagonal antiprismatic duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(8)×I_{2}(12)×A_{1}+, order 384 |

Convex | Yes |

Nature | Tame |

The **octagonal-hexagonal antiprismatic duoprism** or **ohap** is a convex uniform duoprism that consists of 8 hexagonal antiprismatic prisms, 2 hexagonal-octagonal duoprisms, and 12 triangular-octagonal duoprisms. Each vertex joins 2 hexagonal antiprismatic prisms, 3 triangular-octagonal duoprisms, and 1 hexagonal-octagonal duoprism.

## Vertex coordinates[edit | edit source]

The vertices of an octagonal-hexagonal antiprismatic duoprism of edge length 1 are given by all permutations of the first two coordinates of:

## Representations[edit | edit source]

An octagonal-hexagonal antiprismatic duoprism has the following Coxeter diagrams:

- x8o s2s12o (full symmetry; hexagonal antiprisms as alternated dodecagonal prisms)
- x8o s2s6s (hexagonal antiprisms as alternated dihexagonal prisms)
- x4x s2s12o (octagons as ditetragons)
- x4x s2s6s