# Inverted quasiprismatodishexadecachoron

Inverted quasiprismatodishexadecachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Iquipadah |

Elements | |

Cells | 16 tetrahedra, 32 triangular prisms, 16 cubes, 8 octagonal prisms |

Faces | 64 triangles, 32+32+64 squares, 8 octagons |

Edges | 32+32+64+64 |

Vertices | 64 |

Vertex figure | Blend of triangular antipodium and digonal disphenoid |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Tet–3–trip: 150° |

Cube–4–trip: | |

Cube–4–op: 90° | |

Op–8–op: 90° | |

Trip–4–op: | |

Central density | 1 |

Number of external pieces | 80 |

Level of complexity | 30 |

Related polytopes | |

Army | Sidpith |

Regiment | Sidpith |

Conjugate | Great quasiprismatodishexadecachoron |

Convex core | Tesseract |

Abstract & topological properties | |

Flag count | 3072 |

Euler characteristic | –8 |

Orientable | Yes |

Properties | |

Symmetry | B_{2}≀S_{2}, order 128 |

Convex | No |

Nature | Wild |

The **inverted quasiprismatodishexadecachoron**, or **iquipadah**, is a nonconvex uniform polychoron that consists of 16 regular tetrahedra, 32 triangular prisms, 16 cubes, and 8 octagonal prisms. 1 tetrahedron, 3 triangular prisms, 2 cubes, and 2 octagonal prisms meet at each vertex.

It can be created by blending a small disprismatotesseractihexadecachoron with an octagonal diorthoprism, an inscribed compound of 2 square-octagonal duoprisms. In the process 16 cubical cells blend out.

Its vertex figure is concave, a property shared by sanbathi.

Jonathan Bowers wrote that the acronym *iquipadah* occurred to him in church before actually discovering the figure.^{[1]}

## Cross-sections[edit | edit source]

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Category 20: Miscellaneous" (#983).

- Klitzing, Richard. "iquipadah".

## References[edit | edit source]

- ↑ Bowers, Jonathan. Uniform Polychora.