# Great dipentary trishecatonicosachoron

(Redirected from Gidipthi)

Great dipentary trishecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Gidipthi |

Coxeter diagram | o5o3x5/3x5/2*b () |

Elements | |

Cells | 120 icosahedra, 120 small stellated dodecahedra, 120 great dodecicosidodecahedra |

Faces | 2400 triangles, 1440 pentagrams, 720 decagrams |

Edges | 3600+3600 |

Vertices | 1440 |

Vertex figure | Pentagonal frustum, edge lengths 1 (large base), (√5–1)/2 (small base), and √(5–√5)/2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Gaddid–10/3–gaddid: 144° |

Gaddid–5/2–sissid: 144° | |

Gaddid–3–ike: 120° | |

Number of external pieces | 6600 |

Related polytopes | |

Army | Semi-uniform Tex, edge lengths (icosahedra), (surrounded by truncated tetrahedra) |

Regiment | Gidipthi |

Conjugate | Small dipentary trishecatonicosachoron |

Abstract & topological properties | |

Flag count | 86400 |

Euler characteristic | –1560 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

The **great dipentary trishecatonicosachoron**, or **gidipthi**, is a nonconvex uniform polychoron that consists of 120 icosahedra, 120 small stellated dodecahedra, and 120 great dodecicosidodecahedra. 1 icosahedron, 1 small stellated dodecahedron, and 5 great dodecicosidodecahedra join at each vertex.

## Vertex coordinates[edit | edit source]

The vertices of a great dipentary trishecatonicosachoron of edge length 1 are given by all permutations of:

plus all even permutations of:

## Related polychora[edit | edit source]

The great dipentary trishecatonicosachoron is the colonel of a regiment that includes 81 uniform members, as well as 78 fissary uniforms, 18 normal and 59 fissary scaliforms, and 1 scaliform compound.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 22: Gidipthi Regiment" (#1066).

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

- Klitzing, Richard. "gidipthi".