# Faceted rectified icositetrachoron

The **faceted rectified icositetrachoron**, or **frico**, is a nonconvex uniform polychoron that consists of 24 cubes and 24 truncated octahedra. Two cubes and six truncated octahedra join at each vertex.

Faceted rectified icositetrachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Frico |

Coxeter diagram | ()/2 |

Elements | |

Cells | 24 cubes, 24 truncated octahedra |

Faces | 144 squares, 96 hexagons |

Edges | 288 |

Vertices | 96 |

Vertex figure | Triangular retroprism, edge lengths √2 (base) and √3 (sides) |

Edge figure | cube 4 toe 6 toe 6 toe 4 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | 39 |

Dichoral angles | Toe–6–toe: 60° |

Cube–4–toe: 45° | |

Central density | 5 |

Number of external pieces | 1032 |

Level of complexity | 23 |

Related polytopes | |

Army | Rico |

Regiment | Rico |

Conjugate | None |

Convex core | Icositetrachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}, order 1152 |

Convex | No |

Nature | Tame |

## GalleryEdit

## Vertex coordinatesEdit

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

## External linksEdit

- Bowers, Jonathan. "Category 3: Triangular Rectates" (#46).

- Bowers, Jonathan. "Category 6: Sphenoverts" (#46 - recount under tesseractic symmetry).

- Klitzing, Richard. "frico".