# Pentagrammal antiprismatoverted hexacosihecatonicosachoron

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Pentagrammal antiprismatoverted hexacosihecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Papvixhi |

Coxeter diagram | (o3x3x3o5/2*a)/2 |

Elements | |

Cells | 600 truncated tetrahedra, 120 great icosahedra |

Faces | 2400 triangles, 1200 hexagons |

Edges | 3600 |

Vertices | 720 |

Vertex figure | Pentagrammic antiprism, edge lengths 1 (base) and √3 (side) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Tut–6–tut: |

Gike–3–tut: | |

Central density | 17 |

Number of external pieces | 32520 |

Level of complexity | 86 |

Related polytopes | |

Army | Rox |

Regiment | Righi |

Conjugate | Pentagonal retroprismatoverted hexacosihecatonicosachoron |

Convex core | Hexacosichoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

The **pentagrammal antiprismatoverted hexacosihecatonicosachoron**, or **papvixhi**, is a nonconvex uniform polychoron that consists of 120 great icosahedra and 600 truncated tetrahedra. 2 great icosahedra and 10 truncated tetrahedra join at each vertex.

## Vertex coordinates[edit | edit source]

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

## Gallery[edit | edit source]

## External links[edit | edit source]

- Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#90).

- Klitzing, Richard. "papvixhi".