# Quasitruncated great stellated hecatonicosachoron

The **quasitruncated great stellated hecatonicosachoron**, or **quit gishi**, is a nonconvex uniform polychoron that consists of 120 regular icosahedra and 120 quasitruncated great stellated dodecahedra. One icosahedron and five quasitruncated great stellated dodecahedra join at each vertex. As the name suggests, it can be obtained by quasitruncating the great stellated hecatonicosachoron.

Quasitruncated great stellated hecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Quit gishi |

Coxeter diagram | x5/3x3o5o () |

Elements | |

Cells | 120 icosahedra, 120 quasitruncated great stellated dodecahedra |

Faces | 2400 triangles, 720 decagrams |

Edges | 720+3600 |

Vertices | 1440 |

Vertex figure | Pentagonal pyramid, edge lengths 1 (base) and √(5–√5)/2 (side) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Quit gissid–10/3–quit gissid: 144° |

Quit gissid–3–ike: 60° | |

Central density | —20 |

Number of external pieces | 35040 |

Level of complexity | 120 |

Related polytopes | |

Army | Semi-uniform Tex |

Regiment | Quit gishi |

Conjugate | Truncated grand hecatonicosachoron |

Convex core | Hecatonicosachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

## GalleryEdit

## Vertex coordinatesEdit

The vertices of a quasitruncated great stellated hecatonicosachoron of edge length 1 are given by all permutations of:

plus all even permutations of:

## Related polychoraEdit

The quasitruncated great stellated hecatonicosachoron is the colonel of a two-member regiment that also includes the quasitruncated grand stellated hecatonicosachoron.

## External linksEdit

- Bowers, Jonathan. "Category 2: Truncates" (#36).

- Klitzing, Richard. "quit gishi".