# Small hecatonicosafaceted prismatohecatonicosihexacosichoron

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Small hecatonicosafaceted prismatohecatonicosihexacosichoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Shif phix |

Elements | |

Cells | 600 tetrahedra, 720 pentagonal prisms, 120 small rhombicosidodecahedra |

Faces | 2400 triangles, 3600 squares, 1440 pentagons |

Edges | 3600+3600 |

Vertices | 2400 |

Vertex figure | Irregular triangular hemiantipodium, edge lengths 1 (top triangle), (1+√5)/2 (base pseudo-triangle), and √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Dichoral angles | Srid–4–pip: |

Srid–3–tet: | |

Srid–5–pip: 18° | |

Number of external pieces | 8880 |

Level of complexity | 24 |

Related polytopes | |

Army | Sidpixhi |

Regiment | Sidpixhi |

Conjugate | Great hecatonicosafaceted prismatohecatonicosihexacosichoron |

Abstract & topological properties | |

Flag count | 115200 |

Euler characteristic | 1200 |

Orientable | No |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

The **small hecatonicosafaceted prismatohecatonicosihexacosichoron**, or **shif phix**, is a nonconvex uniform polychoron that consists of 600 tetrahedra, 720 pentagonal prisms, and 120 small rhombicosidodecahedra. One tetrahedron, three pentagonal prisms, and three small rhombicosidodecahedra join at each vertex.

It also has 120 dodecahedra and 1200 triangular prisms as pseudofacets.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Category 11: Antipodiumverts" (#455).