# Inverted prismatoicositetrachoron

The **inverted prismatoicositetrachoron**, or **ipi**, is a nonconvex uniform polychoron that consists of 24 small rhombicuboctahedra and 96 triangular prisms. Four small rhombicuboctahedra and four triangular prisms join at each vertex.

Inverted prismatoicositetrachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Ipi |

Elements | |

Cells | 96 triangular prisms, 24 small rhombicuboctahedra |

Faces | 192 triangles, 72+288 squares |

Edges | 288+288 |

Vertices | 144 |

Vertex figure | Blend of two wedges, edge lengths 1 (blended wedge bases) and √2 (sides and top edges of wedges) |

Measures (edge length 1) | |

Circumradius | |

Dichoral angles | Sirco–4–sirco: 90° |

Sirco–4–trip: | |

Sirco–3–trip: 30° | |

Number of external pieces | 600 |

Level of complexity | 19 |

Related polytopes | |

Army | Spic |

Regiment | Spic |

Conjugate | Retroinverted prismatoicositetrachoron |

Abstract & topological properties | |

Flag count | 8064 |

Euler characteristic | 0 |

Orientable | No |

Properties | |

Symmetry | F_{4}, order 1152 |

Flag orbits | 7 |

Convex | No |

Nature | Tame |

It can be constructed as the blend of 3 small rhombated tesseracts, with the octahedral cells blending out.

## Vertex coordinates edit

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

## External links edit

- Bowers, Jonathan. "Category 13: Spic and Giddic Regiments" (#520).

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