# Compound of six pentagonal prisms

(Redirected from Rhombidodecahedron)

Compound of six pentagonal prisms | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Kred |

Elements | |

Components | 6 pentagonal prisms |

Faces | 30 squares, 12 pentagons |

Edges | 30+60 |

Vertices | 60 |

Vertex figure | Isosceles triangle, edge lengths (1+√5)/2, √2, √2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 4–4: 108° |

4–5: 90° | |

Central density | 6 |

Number of external pieces | 180 |

Level of complexity | 34 |

Related polytopes | |

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

Regiment | Kred |

Dual | Compound of six pentagonal tegums |

Conjugate | Compound of six pentagrammic prisms |

Convex core | Dodecahedron |

Abstract & topological properties | |

Flag count | 360 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}+, order 60 |

Convex | No |

Nature | Tame |

The **chirorhombidodecahedron**, **rhombidodecahedron**, **kred**, or **compound of six pentagonal prisms** is a uniform polyhedron compound. It consists of 30 squares and 12 pentagons, with one pentagon and two squares joining at a vertex.

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

## Vertex coordinates[edit | edit source]

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

- ,

Plus all even permutations of:

- ,
- .

## Related polyhedra[edit | edit source]

This compound is chiral. The compound of the two enantiomorphs is the disrhombidodecahedron.

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C7: Chiral and Doubled Prismatics" (#40).

- Klitzing, Richard. "kred".
- Wikipedia contributors. "Compound of six pentagonal prisms".