# Great complex icosidodecahedral alterprism

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Great complex icosidodecahedral alterprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Coxeter diagram | xo3/2xx3/2ox5/2*a&#x |

Elements | |

Cells | 2 great icosahedra 2 small stellated dodecahedra 12 pentagrammic antiprisms 20 octahedra |

Faces | 40+120 triangles 24 pentagrams |

Edges | 60 4-fold 60 6-fold |

Vertices | 24 |

Vertex figure | Exotic faceting of a non-uniform pentagonal antiprism |

Measures (edge length 1) | |

Circumradius | √2/2 ≈ 0.70711 |

Height | √2√5-2/2 ≈ 0.78615 |

Related polytopes | |

Army | Semi-uniform Ipe |

Regiment | Hossdap |

Abstract & topological properties | |

Orientable | No |

Properties | |

Symmetry | H3×A1, order 240 |

Convex | No |

Nature | Exotic |

The **great complex icosidodecahedral alterprism** is an exotic-combo-celled uniform polychoron that consists of 2 great icosahedra, 2 small stellated dodecahedra, 12 pentagrammic antiprisms, and 20 octahedra. The great icosahedra and small stellated dodecahedra lie in the same hyperplanes, forming great complex icosidodecahedron combo-cells. The octahedra go through the centre of the polychoron.

## Vertex coordinates[edit | edit source]

The vertices of a great complex icosidodecahedral alterprism of edge length 1 are given by all even permutations of the first three coordinates of: