# Decagonal-square antiprismatic duoprism

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Decagonal-square antiprismatic duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Dasquap |

Coxeter diagram | x10o s2s8o () |

Elements | |

Tera | 10 square antiprismatic prisms, 8 triangular-decagonal duoprisms, 2 square-decagonal duoprisms |

Cells | 80 triangular prisms, 20 cubes, 10 square antiprisms, 8+8 decagonal prisms |

Faces | 80 triangles, 20+80+80 squares, 8 decagons |

Edges | 80+80+80 |

Vertices | 80 |

Vertex figure | Isosceles-trapezoidal scalene, edge lengths 1, 1, 1, √2 (base trapezoid), √(5+√5)/2 (top), √2 (side edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Squappip–squap–squappip: 144° |

Tradedip–dip–tradedip: = | |

Tradedip–dip–squadedip: = | |

Tradedip–trip–squappip: 90° | |

Squadedip–cube–squappip: 90° | |

Height | |

Central density | 1 |

Number of external pieces | 20 |

Level of complexity | 40 |

Related polytopes | |

Army | Dasquap |

Regiment | Dasquap |

Dual | Decagonal-square antitegmatic duotegum |

Conjugate | Decagrammic-square antiprismatic duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(10)×I_{2}(8)×A_{1}+, order 320 |

Convex | Yes |

Nature | Tame |

The **decagonal-square antiprismatic duoprism** or **dasquap** is a convex uniform duoprism that consists of 10 square antiprismatic prisms, 2 square-decagonal duoprisms, and 8 triangular-decagonal duoprisms. Each vertex joins 2 square antiprismatic prisms, 3 triangular-decagonal duoprisms, and 1 square-decagonal duoprism.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

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

- x10o s2s8o (full symmetry; square antiprisms as alternated octagonal prisms)
- x10o s2s4s () (square antiprisms as alternated ditetragonal prisms)
- x5x s2s8o () (decagons as dipentagons)
- x5x s2s4s ()