# Great retrosphenoverted hecatonicosidishecatonicosachoron

The **great retrosphenoverted hecatonicosidishecatonicosachoron**, or **grawv hidy**, is a nonconvex uniform polychoron that consists of 120 dodecadodecahedra, 120 truncated great icosahedra, and 120 icosidodecadodecahedra. 1 dodecadodecahedron, 2 truncated great icosahedra, and 2 icosidodecadodecahedra join at each vertex.

Great retrosphenoverted hecatonicosidishecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Grawv hidy |

Coxeter diagram | o5/2x3x5/3o5*b () |

Elements | |

Cells | 120 dodecadodecahedra, 120 truncated great icosahedra, 120 icosidodecadodecahedra |

Faces | 1440 pentagons, 720+1440 pentagrams, 2400 hexagons |

Edges | 3600+7200 |

Vertices | 3600 |

Vertex figure | Crossed wedge, edge lengths (√5–1)/2 (two edges of base rectangle and top edge), (1+√5)/2 (other 2 base edges), and √3 (side edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Ided–5–did: 108° |

Did–5/2–tiggy: 108° | |

Ided–5/2–ided: 72° | |

Ided–6–tiggy: 60° | |

Related polytopes | |

Army | Srahi |

Regiment | Sirgashi |

Conjugate | Small retrosphenoverted hecatonicosidishecatonicosachoron |

Abstract & topological properties | |

Euler characteristic | –1560 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

## Vertex coordinates edit

Its vertices are the same as those of its regiment colonel, the small rhombated grand stellated hecatonicosachoron.

## External links edit

- Bowers, Jonathan. "Category 6: Sphenoverts" (#208).

- Klitzing, Richard. "grawv hidy".