# Octagonal-square antiprismatic duoprism

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Octagonal-square antiprismatic duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Osquap |

Coxeter diagram | x8o s2s8o |

Elements | |

Tera | 8 square antiprismatic prisms, 8 triangular-octagonal duoprisms, 2 square-octagonal duoprisms |

Cells | 64 triangular prisms, 16 cubes, 8 square antiprisms, 8+8 octagonal prisms |

Faces | 64 triangles, 16+64+64 squares, 8 octagons |

Edges | 64+64+64 |

Vertices | 64 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Squappip–squap–squappip: 135° |

Todip–op–todip: = | |

Todip–op–sodip: = | |

Todip–trip–squappip: 90° | |

Sodip–cube–squappip: 90° | |

Central density | 1 |

Number of external pieces | 18 |

Level of complexity | 40 |

Related polytopes | |

Army | Osquap |

Regiment | Osquap |

Dual | Octagonal-square antitegmatic duotegum |

Conjugate | Octagrammic-square antiprismatic duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(8)×I_{2}(8)×A_{1}+, order 256 |

Convex | Yes |

Nature | Tame |

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

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

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

- x8o s2s8o (full symmetry; square antiprisms as alternated octagonal prisms)
- x8o s2s4s (square antiprisms as alternated ditetragonal prisms)
- x4x s2s8o (octagons as ditetragons)
- x4x s2s4s