# Prismatoprismatohecatonicosachoron

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Prismatoprismatohecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Paphi |

Elements | |

Cells | 1200 triangular prisms, 720 pentagonal prisms, 120 small dodecicosidodecahedra |

Faces | 2400 triangles, 3600 squares, 1440 pentagons, 720 decagons |

Edges | 3600+3600 |

Vertices | 2400 |

Vertex figure | Inverted triangular antipodium, edge lengths 1 (top base), (1+√5)/2 (bottom base), √2 (side edges of triangles), and √(5+√5)/2 (side edges of crossed trapezoids) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Pip–4–trip: |

Saddid–3–trip: 150° | |

Saddid–10–saddid: 144° | |

Saddid–5–pip: 18° | |

Number of external pieces | 5880 |

Level of complexity | 17 |

Related polytopes | |

Army | Sidpixhi |

Regiment | Sidpixhi |

Conjugate | Disprismatointercepted hecatonicosachoron |

Abstract & topological properties | |

Euler characteristic | 1320 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Wild |

The **prismatoprismatohecatonicosachoron**, or **paphi**, is a nonconvex uniform polychoron that consists of 720 pentagonal prisms, 1200 triangular prisms, and 120 small dodecicosidodecahedra. Three pentagonal prisms, three triangular prisms, and three small dodecicosidodecahedra join at each vertex.

It also has 120 dodecahedra and 600 tetrahedra as pseudofacets.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the small disprismatohexacosihecatonicosachoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 11: Antipodiumverts" (#458).