# Rectified grand stellated hecatonicosachoron

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Rectified grand stellated hecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Ragashi |

Coxeter diagram | o5/2x5o5/2o () |

Elements | |

Cells | 120 great dodecahedra, 120 dodecadodecahedra |

Faces | 1440 pentagons, 720 pentagrams |

Edges | 3600 |

Vertices | 720 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Gad–5–did: 108° |

Did–5/2–did: 72° | |

Central density | 66 |

Number of pieces | 37440 |

Level of complexity | 128 |

Related polytopes | |

Army | Rox |

Regiment | Ragishi |

Conjugate | Rectified great hecatonicosachoron |

Convex core | Hecatonicosachoron |

Abstract properties | |

Euler characteristic | –960 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

The **rectified grand stellated hecatonicosachoron**, or **ragashi**, is a nonconvex uniform polychoron that consists of 120 great dodecahedra and 120 dodecadodecahedra. Two great dodecahedra and five dodecadodecahedra join at each pentagrammic prismatic vertex. As the name suggests, it can be obtained by rectifying the grand stellated hecatonicosachoron.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the rectified great stellated hecatonicosachoron.

## Related polytopes[edit | edit source]

The rectified grand stellated hecatonicosachoron is the base of the 5D scaliform rectified grand stellated hecatonicosachoric alterprism.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#104).

- Klitzing, Richard. "ragashi".