# Compound of five quasitruncated hexahedra

The **quasitruncated rhombihedron**, **quasihyperhombicosicosahedron**, **quitar**, or **compound of five quasitruncated hexahedra** is a uniform polyhedron compound. It consists of 40 triangles (which form coplanar pairs combining into 20 hexagrams) and 30 octagrams, with one triangle and two octagrams joining at each vertex. As the name suggests, it can be derived as the quasitruncation of the rhombihedron, the compound of five cubes.

Compound of five quasitruncated hexahedra | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Quitar |

Elements | |

Components | 5 quasitruncated hexahedra |

Faces | 40 triangles as 20 hexagrams, 30 octagrams |

Edges | 60+120 |

Vertices | 120 |

Vertex figure | Isosceles triangle, edge lengths 1. √2–√2, √2–√2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 8/3–8/3: 90° |

8/3–3: | |

Central density | 35 |

Number of external pieces | 1320 |

Level of complexity | 86 |

Related polytopes | |

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

Regiment | Quitar |

Dual | Compound of five great triakis octahedra |

Conjugate | Compound of five truncated cubes |

Convex core | Icosahedron |

Abstract & topological properties | |

Flag count | 720 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

## Gallery edit

## Vertex coordinates edit

The vertices of a quasitruncated rhombihedron of edge length 1 can be given by all permutations of:

along with all even permutations of:

## External links edit

- Bowers, Jonathan. "Polyhedron Category C2: Compound Truncates" (#11).

- Klitzing, Richard. "quitar".
- Wikipedia contributors. "Compound of five stellated truncated hexahedra".