# Quasiprismatohecatonicosachoron

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Quasiprismatohecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Quiphi |

Coxeter diagram | (x5/2o5o5/3x)/2 (/2) |

Elements | |

Cells | 720 pentagrammic prisms, 120 small stellated dodecahedra |

Faces | 1800 squares, 1440 pentagrams |

Edges | 3600 |

Vertices | 720 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Sissid–5/2–stip: 54° |

Stip–4–stip: | |

Central density | –505 |

Number of external pieces | 767040 |

Level of complexity | 2423 |

Related polytopes | |

Army | Rox |

Regiment | Rigfix |

Conjugate | Small prismatohecatonicosachoron |

Convex core | Joined hexacosichoron |

Abstract & topological properties | |

Euler characteristic | –480 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

The **quasiprismatohecatonicosachoron**, or **quiphi**, is a nonconvex uniform polychoron that consists of 120 small stellated dodecahedra and 720 pentagrammic prisms. 2 small stellated dodecahedra and 10 pentagrammic prisms join at each vertex.

It is in the same regiment as the rectified great faceted hexacosichoron.

A double cover of this polychoron can be formed by pushing the cells of the grand stellated hecatonicosachoron inward.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the rectified great faceted hexacosichoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#121).

- Klitzing, Richard. "quiphi".