# Great rhombic trisicositetrachoron

The **great rhombic trisicositetrachoron**, or **girti**, is a nonconvex uniform polychoron that consists of 24 great rhombihexahedra, 24 cuboctatruncated cuboctahedra, and 24 great rhombicuboctahedra. One great rhombihexahedron, two cuboctatruncated cuboctahedra, and two great rhombicuboctahedra join at each vertex.

Great rhombic trisicositetrachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Girti |

Elements | |

Cells | 24 great rhombihexahedra, 24 great rhombicuboctahedra, 24 cuboctatruncated cuboctahedra |

Faces | 288 squares, 192 hexagons, 144 octagons, 144 octagrams |

Edges | 288+576+576 |

Vertices | 576 |

Vertex figure | Butterfly pyramid, base edge lengths √2–√2, √2, √2–√2, √2; lateral edge lengths √3, √3, √2+√2, √2+√2 |

Measures (edge length 1) | |

Circumradius | |

Dichoral angles | Groh–8/3–cotco: 135° |

Groh–4–girco: 90° | |

Cotco–8–girco: 90° | |

Cotco–6–girco: 60° | |

Related polytopes | |

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

Regiment | Ditdi |

Conjugate | Small rhombic trisicositetrachoron |

Abstract & topological properties | |

Flag count | 18432 |

Euler characteristic | –168 |

Orientable | No |

Properties | |

Symmetry | F_{4}, order 1152 |

Convex | No |

Nature | Tame |

It can be constructed as a blend of three tesseractihexadecatruncated prismatotesseractihexadecachora. In the process the truncated octahedra blend out, while the octagrammic prisms blend into great rhombihexahedra.

## Vertex coordinates edit

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

## External links edit

- Bowers, Jonathan. "Category 10: Prismatorhombates" (#414).