# Antirhombicosicosahedron

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.

Antirhombicosicosahedron | |
---|---|

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 |

Regiment | Arie |

Dual | Compound of five rhombic dodecahedra |

Conjugate | Antirhombicosicosahedron |

Convex core | Rhombic triacontahedron |

Abstract & topological properties | |

Flag count | 480 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

It can be thought of as a rectification of either the small icosicosahedron or the rhombihedron, or the cantellation of the chiricosahedron.

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

## GalleryEdit

## Vertex coordinatesEdit

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

## External linksEdit

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

- Klitzing, Richard. "arie".

- Wikipedia Contributors. "Compound of five cuboctahedra".