# Quasitruncated great stellated hecatonicosachoron

(Redirected from Quit gishi)

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

Rank | 4 |

Type | Uniform |

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 angle | 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, edge lengths (icosahedra), (surrounded by truncated tetrahedra) |

Regiment | Quit gishi |

Conjugate | Truncated grand hecatonicosachoron |

Convex core | Hecatonicosachoron |

Abstract & topological properties | |

Flag count | 57600 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Flag orbits | 4 |

Convex | No |

Nature | Tame |

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.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

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

- ,

plus all even permutations of:

- ,
- ,
- ,
- ,
- ,
- ,
- ,
- .

## Related polychora[edit | edit source]

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

## External links[edit | edit source]

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

- Klitzing, Richard. "quit gishi".