# Rhombihyperhombicosicosahedron

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Rhombihyperhombicosicosahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Rahrie |

Elements | |

Components | 5 small cubicuboctahedra |

Faces | 40 triangles as 20 hexagrams, 30 squares, 30 octagons |

Edges | 120+120 |

Vertices | 120 |

Vertex figure | Crossed isosceles trapezoid, edge lengths 1, √2+√2, √2, √2+√2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 8–4: 90° |

8–3: | |

Central density | 10 |

Number of external pieces | 1470 |

Level of complexity | 112 |

Related polytopes | |

Army | Semi-uniform Grid |

Regiment | Rasseri |

Dual | Compound of five small hexacronic icositetrahedra |

Conjugate | Rhombiquasihyperrhombicosicosahedron |

Convex core | Rhombic triacontahedron |

Abstract & topological properties | |

Flag count | 960 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **rhombihyperhombicosicosahedron**, **rahrie**, or **compound of five small cubicuboctahedra ** is a uniform polyhedron compound. It consists of 40 triangles (which form coplanar pairs combining into 20 hexagrams), 30 squares, and 30 octagons, with one triangle, one square, and two octagons joining at each vertex.

It can be formed by replacing each small rhombicuboctahedron in the rhombisnub rhombicosicosahedron with the small cubicuboctahedron with which it shares its edge skeleton.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the rhombisnub rhombicosicosahedron.

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C3: Fivers" (#16).

- Klitzing, Richard. "rahrie".

- Wikipedia Contributors. "Compound of five small cubicuboctahedra".