# Compound of three cubes

Compound of three cubes | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Rah |

Elements | |

Components | 3 cubes |

Faces | 6+12 squares |

Edges | 12+24 |

Vertices | 24 |

Vertex figure | Equilateral triangle, edge length √2 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Volume | 3 |

Dihedral angle | 90° |

Central density | 3 |

Number of external pieces | 120 |

Level of complexity | 17 |

Related polytopes | |

Army | Semi-uniform Toe, edge lengths (squares), (between ditrigons) |

Regiment | Rah |

Dual | Compound of three octahedra |

Conjugate | Compound of three cubes |

Convex core | Chamfered cube |

Abstract & topological properties | |

Flag count | 144 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}, order 48 |

Flag orbits | 3 |

Convex | No |

Nature | Tame |

The **rhombihexahedron**, **rah**, or **compound of three cubes** is a uniform polyhedron compound. It consists of 6+12 squares, with three faces joining at a vertex.

A complete double cover of this compound is a special case of the general rhombisnub dishexahedron.

The cube components each have square prismatic symmetry. In fact this compound can be constructed by starting with three fully coincident cubes and rotating one 45º along each of the 4-fold symmetry axes.

Its quotient prismatic equivalent is the square axial prismatic trigyroprism, which is five-dimensional.

It is one of three uniform polyhedron compounds that is kaleidoscopic, along with the stella octangula and truncated stella octangula.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

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

- .

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C5: Tets and Cubes" (#29).

- Klitzing, Richard. "rah".
- Wikipedia contributors. "Compound of three cubes".