# Compound of six decagonal prisms

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Compound of six decagonal prisms | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Rassid |

Elements | |

Components | 6 decagonal prisms |

Faces | 60 squares, 12 decagons |

Edges | 60+60+60 |

Vertices | 120 |

Vertex figure | Isosceles triangle, edge length √(5+√5)/2, √2, √2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 4–4: 144° |

4–10: 90° | |

Central density | 6 |

Number of external pieces | 600 |

Level of complexity | 34 |

Related polytopes | |

Army | Semi-uniform Grid, edge lengths (dipentagon-ditrigon), (dipentagon-rectangle), (ditrigon-rectangle) |

Regiment | Rassid |

Dual | Compound of six decagonal tegums |

Conjugate | Compound of six decagrammic prisms |

Convex core | Dodecahedron |

Abstract & topological properties | |

Flag count | 720 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **rhombisnub dodecahedron**, **rassid**, or **compound of six decagonal prisms** is a uniform polyhedron compound. It consists of 60 squares and 12 decagons, with one decagon and two squares joining at a vertex.

Its quotient prismatic equivalent is the dipentagonal trapezoprismatic hexateroorthowedge, which is eight-dimensional.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a rhombisnub dodecahedron of edge length 1 are given by all even permutations of:

- ,
- ,
- ,
- ,
- .

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C6: Prismatics" (#36).

- Klitzing, Richard. "rassid".
- Wikipedia contributors. "Compound of six decagonal prisms".