# Faceted rectified hexacosichoron

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Faceted rectified hexacosichoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Frox |

Coxeter diagram | x3o3/2x5o -600 2thah |

Elements | |

Cells | |

Faces | |

Edges | 3600 |

Vertices | 720 |

Vertex figure | Pentagrammic toroprism |

Edge figure | id.id.pip.pip.pip |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Central density | 1 |

Number of external pieces | 40680 |

Level of complexity | 80 |

Related polytopes | |

Army | Rox |

Regiment | Rox |

Conjugate | Retroinverted prismatohecatonicosachoron |

Convex core | Hecatonicosachoron |

Abstract & topological properties | |

Flag count | 72000 |

Euler characteristic | 720 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Flag orbits | 5 |

Convex | No |

Nature | Tame |

The **faceted rectified hexacosichoron**, or **frox**, is a nonconvex uniform polychoron that consists of 120 icosidodecahedra and 720 pentagonal prisms. 5 icosidodecahedra and 10 pentagonal prisms join at each vertex.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#77).

- Klitzing, Richard. "frox".