# Inverted prismatoicositetrachoron

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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 |

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.

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

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

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

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