# Grand ditetrahedronary hexacosidishecatonicosachoron

Grand ditetrahedronary hexacosidishecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Gadtaxady |

Coxeter diagram | x3o3o3o5/2*a () |

Elements | |

Cells | 600 tetrahedra, 120 great stellated dodecahedra, 120 great icosidodecahedra |

Faces | 2400 triangles, 1440 pentagrams |

Edges | 3600 |

Vertices | 600 |

Vertex figure | Rhombitetratetrahedron, edge lengths 1 and (√5–1)/2 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Gid–3–tet: |

Gissid–5/2–gid: 144° | |

Central density | 34 |

Number of pieces | 8520 |

Level of complexity | 26 |

Related polytopes | |

Army | Hi |

Regiment | Gadtaxady |

Company | Gadtaxady |

Conjugate | Small retroditetrahedronary hexacosidishecatonicosachoron |

Abstract properties | |

Euler characteristic | 0 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

The **grand ditetrahedronary hexacosidishecatonicosachoron**, or **gadtaxady**, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 great stellated dodecahedra, and 120 great icosidodecahedra. 4 great stellated dodecahedra, 4 tetrahedra, and 6 great icosidodecahedra join at each vertex, with a small rhombitetratetrahedron as the vertex figure.

The grand ditetrahedronary hexacosidishecatonicosachoron contains the vertices of a great dodecicosidodecahedral prism and decagrammic duoprism.

## Cross-sections[edit | edit source]

## Vertex coordinates[edit | edit source]

The vertices of a grand ditetrahedronary hexacosidishecatonicosachoron of edge length 1, centered at the origin, are given by all permutations of:

together with all the even permutations of:

## Related polychora[edit | edit source]

The grand ditetrahedronary hexacosidishecatonicosachoron is the colonel of a regiment with 37 members, plus 5 fissaries and three compounds (two are subsymmetric), as well as 11 scaliform members plus 54 scaliform fissaries and 2 scaliform compounds.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 18: Ditetrahedrals" (#852).

- Bowers, Jonathan. "How to Make Gadtaxady".

- Klitzing, Richard. "gadtaxady".