# Grand ditetrahedronary hexacosihecatonicosachoron

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Grand ditetrahedronary hexacosihecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Gadtaxhi |

Coxeter diagram | o3o3o5x3/2*b () |

Elements | |

Cells | 600 tetrahedra, 120 great ditrigonary icosidodecahedra |

Faces | 2400 triangles, 720 pentagons |

Edges | 3600 |

Vertices | 600 |

Vertex figure | Quasitruncated tetrahedron, edge lengths 1 (triangle edges) and (1+√5)/2 (other edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Gidtid–3–tet: |

Gidtid–5–gidtid: 72° | |

Central density | 218 |

Number of external pieces | 78000 |

Level of complexity | 261 |

Related polytopes | |

Army | Hi |

Regiment | Gadtaxady |

Conjugate | Small ditetrahedronary hexacosihecatonicosachoron |

Abstract & topological properties | |

Euler characteristic | –600 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

The **grand ditetrahedronary hexacosihecatonicosachoron**, or **gadtaxhi**, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra and 120 great ditrigonary icosidodecahedra. 4 great ditrigonary icosidodecahedra and 4 tetrahedra join at each vertex.

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Category 18: Ditetrahedrals" (#856).

- Klitzing, Richard. "gadtaxhi".