# Retroinverted prismatohecatonicosachoron

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Retroinverted prismatohecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Ripahi |

Elements | |

Cells | 120 gid, 720 stip |

Faces | 1200 triangles, 1800 squares, 1440 pentagrams |

Edges | 3600 |

Vertices | 720 |

Vertex figure | Pentagonal toroprism |

Measures (edge length 1) | |

Circumradius | |

Number of external pieces | 92880 |

Level of complexity | 184 |

Related polytopes | |

Army | Rox |

Regiment | Rigfix |

Conjugate | Frox |

Convex core | Joined hexacosichoron |

Abstract & topological properties | |

Euler characteristic | 720 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

The **retroinverted prismatohecatonicosachoron**, or **ripahi**, is a nonconvex uniform polychoron that consists of 120 great icosidodecahedra and 720 pentagrammic prisms. Five great icosidodecahedra and ten pentagrammic prisms join at each vertex.

It also has small stellated dodecahedra as pseudofacets.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#123).

- Klitzing, Richard. "ripahi".

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