# Small quasidisprismatohexacosihecatonicosachoron

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Small quasidisprismatohexacosihecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Saquid paxhi |

Coxeter diagram | x5o3o3/2x () |

Elements | |

Cells | 600 tetrahedra, 1200 triangular prisms, 720 pentagonal prisms, 120 dodecahedra |

Faces | 2400 triangles, 3600 squares, 1440 pentagons |

Edges | 3600 |

Vertices | 600 |

Vertex figure | Compound of 4 triangular retroantipodiums, edge lengths 1 (small base), (1+√5)/2 (large base), and √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Doe–5–pip: 18° |

Pip–4–trip: | |

Tet–3–trip: | |

Related polytopes | |

Army | Hi |

Regiment | Sidtaxhi |

Conjugate | Quasidisprismatogrand hexacosihecatonicosachoron |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Feral |

The **small quasidisprismatohexacosihecatonicosachoron**, or **saquid paxhi**, is a nonconvex fissary uniform polychoron that consists of 600 regular tetrahedra, 120 regular dodecahedra, 1200 triangular prisms, and 720 pentagonal prisms. 4 tetrahedra, 4 dodecahedra, 12 triangular prisms, and 12 pentagonal prisms join at each vertex. It is the result of pushing the cells of either a hecatonicosachoron or a hexacosichoron inwards.

It is fissary as vertices coincide by four, producing a compound vertex figure; in addition, edges coincide by two.

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the small ditetrahedronary hexacosihecatonicosachoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 18: Ditetrahedrals" (#F11).

- Klitzing, Richard. "saquid paxhi".