# Rectified great faceted hexacosichoron

Rectified great faceted hexacosichoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Rigfix |

Coxeter diagram | o5o5/2x3o () |

Elements | |

Cells | 120 small stellated dodecahedra, 120 great icosidodecahedra |

Faces | 1200 triangles, 1440 pentagrams |

Edges | 3600 |

Vertices | 720 |

Vertex figure | Semi-uniform pentagonal prism, edge lengths (√5–1)/2 (base) and 1 (side) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Gid–3–gid: 120° |

Sissid–5/2–gid: 108° | |

Central density | 76 |

Number of external pieces | 5040 |

Level of complexity | 24 |

Related polytopes | |

Army | Rox, edge length |

Regiment | Rigfix |

Conjugate | Rectified faceted hexacosichoron |

Convex core | Hecatonicosachoron |

Abstract & topological properties | |

Flag count | 43200 |

Euler characteristic | –480 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

The **rectified great faceted hexacosichoron**, or **rigfix**, is a nonconvex uniform polychoron that consists of 120 small stellated dodecahedra and 120 great icosidodecahedra. Two small stellated dodecahedra and five great icosidodecahedra join at each pentagonal prismatic vertex. As the name suggests, it can be obtained by rectifying the great faceted hexacosichoron.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

The vertices of a rectified great faceted hexacosichoron of edge length 1 are given by all permutations of:

along with even permutations of:

## Related polychora[edit | edit source]

The rectified great faceted hexacosichoron is the colonel of a regiment with 15 members. Of these, one other besideds the colonel itself is Wythoffian (the rectified grand hexacosichoron), two are hemi-Wythoffian (the great pentagrammal antiprismatoverted dishecatonicosachoron and quasiprismatohecatonicosachoron), and one is noble (the grand retropental hecatonicosachoron).

Uniform polychoron compounds composed of rectified great faceted hexacosichora include:

- Rectified great faceted chirotetrahedral dishexacosichoron (2)
- Rectified great faceted snub pentishecatonicosachoron (5)
- Rectified great faceted snub decahecatonicosachoron (10)

## External links[edit | edit source]

- Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#118).

- Klitzing, Richard. "rigfix".