# Pentagonal-prismatic heptacosiicosachoron

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Pentagonal-prismatic heptacosiicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Paphacki |

Elements | |

Cells | 720 pentagonal prisms |

Faces | 1800 squares, 720 pentagons |

Edges | 1200 |

Vertices | 120 |

Vertex figure | Great noble triangular hexecontahedron |

Edge figure | (pip 4 pip 4 pip 5)×3 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Volume | |

Number of external pieces | 1260000 |

Level of complexity | 3490 |

Related polytopes | |

Army | Ex |

Regiment | Sishi |

Conjugate | Pentagrammic-prismatic heptacosiicosachoron |

Convex core | Joined hecatonicosachoron |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | H4, order 14400 |

Convex | No |

Nature | Feral |

The **pentagonal-prismatic heptacosiicosachoron**, or **paphacki**, is a noble uniform polychoron in the small stellated hecatonicosachoron's regiment. It consists of 720 pentagonal prisms, 60 of which meet at each of its 120 vertices.

## Vertex coordinates[edit | edit source]

The vertices of a pentagonal-prismatic heptacosiicosachoron of unit edge length are given by:

and all even permutations of:

The first two sets of vertices form a unit icositetrachoron that can be inscribed into the small stellated hecatonicosachoron. This corresponds to the fact there is a compound of 25 icositetrachora with the same vertices and edges as the small stellated hecatonicosachoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 17: Sishi Regiment" (#769).
- Klitzing, Richard. "Paphacki".