# Icositetrintercepted icositetrachoron

The **icositetrintercepted icositetrachoron**, or **ini**, is a nonconvex uniform polychoron that consists of 24 cuboctahedra and 24 truncated octahedra. 3 cuboctahedra and 6 truncated octahedra join at each vertex.

Icositetrintercepted icositetrachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Ini |

Elements | |

Cells | |

Faces | 96 triangles, 144 squares, 96 hexagons |

Edges | 288 |

Vertices | 96 |

Vertex figure | Triangular toroprism, edge lengths √2 (base edges), 1 (side edges of rectaangles), and √3 (side edges of triangles) |

Edge figure | co 3 co 4 toe 6 toe 6 toe 4 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | 68 |

Dichoral angle | Co–3–co: 120° Co–4–toe: 90° Toe–6–toe: 60° |

Central density | 6 |

Number of external pieces | 168 |

Level of complexity | 6 |

Related polytopes | |

Army | Rico |

Regiment | Rico |

Conjugate | None |

Convex core | Icositetrachoron |

Abstract & topological properties | |

Flag count | 5760 |

Euler characteristic | 96 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}, order 1152 |

Flag orbits | 5 |

Convex | No |

Nature | Wild |

It is wild because it has cuboctahedra intercepted by hexagons.

## Cross-sections edit

## Vertex coordinates edit

Its vertices are the same as those of its regiment colonel, the rectified icositetrachoron.

## External links edit

- Bowers, Jonathan. "Category 3: Triangular Rectates" (#47).

- Bowers, Jonathan. "Category 6: Sphenoverts" (#47 - recount under tesseractic symmetry).

- Klitzing, Richard. "ini".