# Great ditrigonary hexacosihecatonicosachoron

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Great ditrigonary hexacosihecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Gidtixhi |

Coxeter diagram | x3o3o3/2o5*b () |

Elements | |

Cells | 600 tetrahedra, 120 icosahedra |

Faces | 2400 triangles |

Edges | 1200 |

Vertices | 120 |

Vertex figure | Great ditrigonary icosidodecahedron, edge length 1 |

Edge figure | (tet 3 ike 3)×3 |

Measures (edge length 1) | |

Circumradius | 1 |

Hypervolume | |

Dichoral angle | |

Central density | 39 |

Number of external pieces | 57600 |

Level of complexity | 154 |

Related polytopes | |

Army | Ex |

Regiment | Sishi |

Company | Sidtixhi |

Dual | Great triambic icosahedral hecatonicosachoron |

Conjugate | Small ditrigonary hexacosihecatonicosachoron |

Abstract & topological properties | |

Euler characteristic | 600 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

The **great ditrigonary hexacosihecatonicosachoron**, or **gidtixhi**, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra and 120 regular icosahedra. 12 icosahedra and 20 tetrahedra join at each vertex, with a great ditrigonary icosidodecahedron as the vertex figure.

It has the same set of triangular faces as the small ditrigonary hexacosihecatonicosachoron.

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the small stellated hecatonicosachoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 17: Sishi Regiment" (#766).

- Klitzing, Richard. "gidtixhi".