# Small prismatohecatonicosachoron

Jump to navigation
Jump to search

Small prismatohecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Sophi |

Coxeter diagram | (x5o5/2o5x)/2 (/2) |

Elements | |

Cells | 720 pentagonal prisms, 120 great dodecahedra |

Faces | 1800 squares, 1440 pentagons |

Edges | 3600 |

Vertices | 720 |

Vertex figure | Pentagrammic antiprism, edge lengths (1+√5)/2 (base) and √2 (side) |

Edge figure | gad.pip.pip.pip |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Gad–5–pip: 162° |

Pip–4–pip: | |

Central density | 3 |

Number of external pieces | 10920 |

Level of complexity | 21 |

Related polytopes | |

Army | Rox |

Regiment | Rox |

Conjugate | Quasiprismatohecatonicosachoron |

Convex core | Chamfered hecatonicosachoron |

Abstract & topological properties | |

Euler characteristic | –480 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

The **small prismatohecatonicosachoron**, or **sophi**, is a nonconvex uniform polychoron that consists of 120 great dodecahedra and 720 pentagonal prisms. 2 great dodecahedra and 10 pentagonal prisms join at each vertex.

A double cover of this polychoron can be formed by expanding the cells of the great hecatonicosachoron outward.

## 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" (#75).

- Klitzing, Richard. "sophi".