# Grand inverted ditetrahedronary trishecatonicosachoron

The **grand inverted ditetrahedronary trishecatonicosachoron**, or **gaid tathi**, is a nonconvex uniform polychoron that consists of 120 great stellated dodecahedra, 120 great icosidodecahedra, and 120 great ditrigonary icosidodecahedra. Four great stellated dodecahedra, six great icosidodecahedra, and four great ditrigonary icosidodecahedra join at each vertex.

Grand inverted ditetrahedronary trishecatonicosachoron | |
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Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Gaid tathi |

Elements | |

Cells | 120 gissid, 120 gid, 120 gidtid |

Faces | 2400 triangles, 720 pentagons, 1440 pentagrams |

Edges | 3600 |

Vertices | 600 |

Measures (edge length 1) | |

Circumradius | |

Number of external pieces | 115320 |

Level of complexity | 279 |

Related polytopes | |

Army | Hi |

Regiment | Gadtaxady |

Conjugate | Small retroinverted ditetrahedronary trishecatonicosachoron |

Abstract & topological properties | |

Flag count | 72000 |

Euler characteristic | 1200 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Wild |

## Vertex coordinates edit

Its vertices are the same as those of its regiment colonel, the grand ditetrahedronary hexacosidishecatonicosachoron.

## External links edit

- Bowers, Jonathan. "Category 18: Ditetrahedrals" (#857).

- Klitzing, Richard. "Gaid tathi".

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