# Compound of twelve pentagonal prisms

(Redirected from Disrhombidodecahedron)

Compound of twelve pentagonal prisms | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Dird |

Elements | |

Components | 12 pentagonal prisms |

Faces | 60 squares, 24 pentagons |

Edges | 60+120 |

Vertices | 60 |

Vertex figure | Compound of two isosceles triangles, edge lengths (1+√5)/2, √2, √2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 4–4: 108° |

4–5: 90° | |

Central density | 12 |

Number of external pieces | 540 |

Level of complexity | 32 |

Related polytopes | |

Army | Semi-uniform Ti, edge lengths (pentagons), (between ditrigons) |

Regiment | Dird |

Dual | Compound of twelve pentagonal tegums |

Conjugate | Compound of twelve pentagrammic prisms |

Convex core | Dodecahedron |

Abstract & topological properties | |

Flag count | 720 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **disrhombidodecahedron**, **dird**, or **compound of twelve pentagonal prisms** is a uniform polyhedron compound. It consists of 60 squares and 24 pentagons, with two pentagons and four squares joining at a vertex.

It can be formed by combining the two chiral forms of the chirorhombidodecahedron, which results in vertices pairing up and two components joining per vertex.

Its quotient prismatic equivalent is the pentagonal prismatic dodecadakoorthowedge, which is fourteen-dimensional.

## Vertex coordinates[edit | edit source]

The vertices of a disrhombidodecahedron of edge length 1 are given by all permutations of:

- ,

Plus all even permutations of:

- ,
- .

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C7: Chiral and Doubled Prismatics" (#41).

- Klitzing, Richard. "dird".
- Wikipedia contributors. "Compound of twelve pentagonal prisms".