# Great tetrisicositetrachoron

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Great tetrisicositetrachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Guti |

Coxeter diagram | x3x4x3o4/3*a () |

Elements | |

Cells | 24 truncated octahedra, 24 truncated cubes, 24 quasirhombicuboctahedra, 24 great rhombicuboctahedra |

Faces | 192 triangles, 144+288 squares, 192 hexagons, 144 octagons |

Edges | 288+576+576 |

Vertices | 576 |

Vertex figure | Crossed isosceles trapezoidal pyramid, base edge lengths 1, √2, √2, √2; lateral edge lengths √3, √3, √2+√2, √2+√2 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Querco–4–toe: 135° |

Querco–4–girco: 90° | |

Querco–3–tic: 60° | |

Toe–6–girco: 60° | |

Tic–8–girco: 45° | |

Central density | 10 |

Related polytopes | |

Army | Semi-uniform Grico, edge lengths (truncated cubes), 1 (sides of triangular prisms) |

Regiment | Ditdi |

Conjugate | Small tetrisicositetrachoron |

Abstract & topological properties | |

Flag count | 18432 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}, order 1152 |

Convex | No |

Nature | Tame |

The **great tetrisicositetrachoron**, or **guti**, is a nonconvex uniform polychoron that consists of 24 truncated octahedra, 24 truncated cubes, 24 quasirhombicuboctahedra, and 24 great rhombicuboctahedra. 1 truncated cube 1 truncated octahedron, 1 quasirhombicuboctahedron, and 2 great rhombicuboctahedra join at each vertex.

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the disicositetratruncated disicositetrachoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 10: Prismatorhombates" (#413).

- Klitzing, Richard. "guti".