# Pseudorhombic great hecatonicosihexacosichoron

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Pseudorhombic great hecatonicosihexacosichoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Pirghix |

Elements | |

Cells | 720 pentagrammic prisms, 600 truncated octahedra, 120 truncated great icosahedra |

Faces | 3600 squares, 1440 pentagrams, 1200+2400 hexagons |

Edges | 3600+7200 |

Vertices | 3600 |

Vertex figure | Isosceles triangular retroprism, dege lengths √2 (4), (√5–1)/2 (2), and √3 (6) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Tiggy–5/2–stip: 126° |

Tiggy–6–toe: | |

Toe–4–stip: | |

Toe–6–toe: | |

Related polytopes | |

Army | Srahi |

Regiment | Sirgashi |

Conjugate | Pseudorhombic small hecatonicosihexacosichoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

The **pseudorhombic great hecatonicosihexacosichoron**, or **pirghix**, is a nonconvex uniform polychoron that consists of 120 truncated great icosahedra, 720 pentagrammic prisms, and 600 truncated octahedra. Two truncated great icosahedra, two pentagrammic prisms, and four truncated octahedra join at each vertex.

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Category 6: Sphenoverts" (#210).