# Compound of five cuboctahedra

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Compound of five cuboctahedra | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Arie |

Elements | |

Components | 5 cuboctahedra |

Faces | 40 triangles as 20 hexagrams, 30 squares |

Edges | 120 |

Vertices | 60 |

Vertex figure | Rectangle, edge lengths 1 and √2 |

Measures (edge length 1) | |

Circumradius | 1 |

Volume | |

Dihedral angle | |

Central density | 5 |

Number of external pieces | 260 |

Level of complexity | 14 |

Related polytopes | |

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

Regiment | Arie |

Dual | Compound of five rhombic dodecahedra |

Conjugate | Compound of five cuboctahedra |

Convex core | Rhombic triacontahedron |

Abstract & topological properties | |

Flag count | 480 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **antirhombicosicosahedron**, **arie**, or **compound of five cuboctahedra** is a uniform polyhedron compound. It consists of 40 triangles (which form coplanar pairs combining into 20 hexagrams) and 30 squares, with two of each joining at a vertex.

It can be thought of as a rectification of either the small icosicosahedron or the rhombihedron, or the cantellation of the chiricosahedron. Each individual component has pyritohedral symmetry.

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

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

The vertices of an antirhombicosicosahedron of edge length 1 can be given by all even permutations of:

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C3: Fivers" (#12).

- Klitzing, Richard. "arie".

- Wikipedia Contributors. "Compound of five cuboctahedra".