# Icositetradiminished great faceted hexacosichoron

Icositetradiminished great faceted hexacosichoron | |
---|---|

Rank | 4 |

Type | Scaliform |

Notation | |

Bowers style acronym | Irgfix |

Elements | |

Cells | 24 gike, 24 sissid, 96 targi |

Faces | 96+96+288 triangles, 288 pentagrams |

Edges | 144+288 |

Vertices | 96 |

Vertex figure | Faceting of tridiminished great icosahedron |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Related polytopes | |

Army | Sadi |

Regiment | Rasdi |

Conjugate | Icositetradiminished faceted hexacosichoron |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | F_{4}/2, order 576 |

Convex | No |

Nature | Coincidic |

The **icositetradiminished great faceted hexacosichoron**, also called the **icositetrareplenished great faceted hexacosichoron** or **irgfix**, is a coincidic scaliform polychoron that consists of 24 great icosahedra, 24 small stellated dodecahedra, and 96 tridiminished great icosahedra. 3 great icosahedra, 3 small stellated dodecahedra, and 9 tridiminished great icosahedra meet at each vertex. It can be formed by diminishing the 24 vertices of an inscribed icositetrachoron from a great faceted hexacosichoron.

The great icosahedra and small stellated dodecahedra lie in the same hyperplanes, forming great complex icosidodecahedron combo-cells, making the polychoron coincidic.

## Vertex coordinates[edit | edit source]

The vertices of an icositetradiminished great faceted hexacosichoron of edge length 1, centered at the origin, are the same as those of the retrosnub disicositetrachoron, given by all even permutations of:

## Related polychora[edit | edit source]

This polychoron has the same edges as the retrosnub disicositetrachoron, and it also has all of its triangles as well as some additional pentagrams.