# Pentagonal-small rhombicosidodecahedral duoprism

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Pentagonal-small rhombicosidodecahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Pesrid |

Coxeter diagram | x5o x5o3x |

Elements | |

Tera | 20 triangular-pentagonal duoprisms, 30 square-pentagonal duoprisms, 12 pentagonal duoprisms |

Cells | 100 triangular prisms, 150 cubes, 60+60+60 pentagonal prisms, 5 small rhombicosidodecahedra |

Faces | 150 triangles, 150+300+300 squares, 60+60 pentagons |

Edges | 300+300+300 |

Vertices | 300 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Trapedip–pip–squipdip: |

Squipdip–pip–pedip: | |

Sriddip–srid–sriddip: 108° | |

Trapedip–trip–sriddip: 90° | |

Squipdip–cube–sriddip: 90° | |

Pedip–pip–sriddip: 90° | |

Central density | 1 |

Number of external pieces | 67 |

Level of complexity | 40 |

Related polytopes | |

Army | Pesrid |

Regiment | Pesrid |

Dual | Pentagonal-deltoidal hexecontahedral duotegum |

Conjugate | Pentagrammic-quasirhombicosidodecahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×H_{2}, order 1200 |

Convex | Yes |

Nature | Tame |

The **pentagonal-small rhombicosidodecahedral duoprism** or **pesrid** is a convex uniform duoprism that consists of 5 small rhombicosidodecahedral prisms, 12 pentagonal duoprisms, 30 square-pentagonal duoprisms, and 20 triangular-pentagonal duoprisms. Each vertex joins 2 small rhombicosidodecahedral prisms, 1 triangular-pentagonal duoprism, 2 square-pentagonal duoprisms, and 1 pentagonal duoprism.

## Vertex coordinates[edit | edit source]

The vertices of a pentagonal-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: