# Quatro-icositetradiminished hexacosichoron

The **quatro-icositetradiminished hexacosichoron**, also known as the **tristellatododecahedral enneacontahexachoron**, is a convex isochoric polychoron with 96 tri-tridiminished icosahedra as cells. It can be obtained as the dual of the snub disicositetrachoron.

Quatro-icositetradiminished hexacosichoron | |
---|---|

Rank | 4 |

Type | Uniform dual |

Notation | |

Bowers style acronym | Quidex |

Coxeter diagram | p3p4o3o () |

Elements | |

Cells | 96 tri-tridiminished icosahedra |

Faces | 288 isosceles triangles, 144 kites |

Edges | 96+96+288 |

Vertices | 24+24+96 |

Vertex figure | 24+96 tetrahedra, 24 dodecahedra |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Snub disicositetrachoron |

Abstract & topological properties | |

Flag count | 5760 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

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

Convex | Yes |

Nature | Tame |

It can also be obtained as an intersection formed by diminishing 4 sets of 24 vertices, each corresponding to an inscribed icositetrachoron from the regular hexacosichoron. Alternatively, it can be constructed by raising tall pyramids on 24 of the cells of the hecatonicosachoron corresponding to the vertices of an icositetrachoron such that adjacent cells merge into tri-tridiminished icosahedra.

Each cell of this polychoron has trigonal symmetry, with 3 kites and 6 isosceles triangles for faces.

## External links edit

- Klitzing, Richard. "Quidex".