# Compound of five truncated cubes

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

Compound of five truncated cubes | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Tar |

Elements | |

Components | 5 truncated cubes |

Faces | 40 triangles as 20 hexagrams, 30 octagons |

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: |

8–8: 90° | |

Central density | 5 |

Number of external pieces | 380 |

Level of complexity | 26 |

Related polytopes | |

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

Regiment | Tar |

Dual | Compound of five triakis octahedra |

Conjugate | Compound of five quasitruncated hexahedra |

Convex core | Rhombic triacontahedron |

Abstract & topological properties | |

Flag count | 720 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

Its quotient prismatic equivalent is the truncated cubic pentachoroorthowedge, which is seven-dimensional.

## Gallery edit

## Vertex coordinates edit

The vertices of a truncated 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" (#10).

- Klitzing, Richard. "tar".
- Wikipedia contributors. "Compound of five truncated cubes".