# Icositetradiminished faceted hexacosichoron

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

Rank | 4 |

Type | Scaliform |

Notation | |

Bowers style acronym | Idfix |

Elements | |

Cells | 24 ike, 24 gad, 96 teddi |

Faces | 96+96+288 triangles, 288 pentagons |

Edges | 144+288 |

Vertices | 96 |

Vertex figure | Faceting of tridiminished icosahedron |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Related polytopes | |

Army | Sadi |

Regiment | Sadi |

Conjugate | Icositetradiminished great faceted hexacosichoron |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

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

Convex | No |

Nature | Coincidic |

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

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

## Vertex coordinates[edit | edit source]

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

## Related polychora[edit | edit source]

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