# Decagonal-small rhombicosidodecahedral duoprism

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Decagonal-small rhombicosidodecahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Dasrid |

Coxeter diagram | x10o x5o3x () |

Elements | |

Tera | 20 triangular-decagonal duoprisms, 30 square-decagonal duoprisms, 12 pentagonal-decagonal duoprisms, 10 small rhombicosidodecahedral prisms |

Cells | 200 triangular prisms, 300 cubes, 120 pentagonal prisms, 60+60 decagonal prisms, 10 small rhombicosidodecahedra |

Faces | 200 triangles, 300+600+600 squares, 120 pentagons, 60 decagons |

Edges | 600+600+600 |

Vertices | 600 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tradedip–dip–squadedip: |

Squadedip–dip–padedip: | |

Sriddip–srid–sriddip: 144° | |

Tradedip–trip–sriddip: 90° | |

Squadedip–cube–sriddip: 90° | |

Padedip–pip–sriddip: 90° | |

Central density | 1 |

Number of external pieces | 72 |

Level of complexity | 40 |

Related polytopes | |

Army | Dasrid |

Regiment | Dasrid |

Dual | Decagonal-deltoidal hexecontahedral duotegum |

Conjugate | Decagrammic-quasirhombicosidodecahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×I_{2}(10), order 2400 |

Convex | Yes |

Nature | Tame |

The **decagonal-small rhombicosidodecahedral duoprism** or **dasrid** is a convex uniform duoprism that consists of 10 small rhombicosidodecahedral prisms, 12 pentagonal-decagonal duoprisms, 30 square-decagonal duoprisms, and 20 triangular-decagonal duoprisms. Each vertex joins 2 small rhombicosidodecahedral prisms, 1 triangular-decagonal duoprism, 2 square-decagonal duoprisms, and 1 pentagonal-decagonal duoprism.

## Vertex coordinates[edit | edit source]

The vertices of a decagonal-small rhombicosidodecahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of:

as well as all even permutations of the last three coordinates of:

## Representations[edit | edit source]

A decagonal-small rhombicosidodecahedral duoprism has the following Coxeter diagrams:

- x10o x5o3x (full symmetry)
- x5x x5o3x (decagons as dipentagons)