# Compound of five cubohemioctahedra

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Compound of five cubohemioctahedra | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Gari |

Elements | |

Components | 5 cubohemioctahedra |

Faces | 30 squares, 20 hexagons as 10 stellated dodecagons |

Edges | 120 |

Vertices | 60 |

Vertex figure | Bowtie, edge lengths √2 and √3 |

Measures (edge length 1) | |

Circumradius | 1 |

Dihedral angle | |

Central density | odd |

Related polytopes | |

Army | Semi-uniform Srid, edge lengths (pentagons), (triangles) |

Regiment | Arie |

Dual | Compound of five hexahemioctacrons |

Conjugate | Compound of five cubohemioctahedra |

Abstract & topological properties | |

Orientable | No |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **great antirhombicosahedron**, **gari**, or **compound of five cubohemioctahedra** is a uniform polyhedron compound. It consists of 30 squares and 20 hexagons (which pair up into 10 stellated dodecagons), with two of each joining at a vertex.

It can be formed by replacing each cuboctahedron in the antirhombicosicosahedron with the cubohemioctahedron 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 antirhombicosicosahedron.

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C3: Fivers" (#14).

- Klitzing, Richard. "gari".
- Wikipedia contributors. "Compound of five cubohemioctahedra".