# Grand rhombic disicositetrachoron

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Grand rhombic disicositetrachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Gardi |

Elements | |

Cells | 24 small rhombihexahedra, 24 great rhombicuboctahedra |

Faces | 288 squares, 96 hexagons, 144 octagons |

Edges | 288+576 |

Vertices | 288 |

Vertex figure | Crossed butterfly wedge, dege lengths √2 (4), √3 (2), and √2+√2 (4) |

Measures (edge length 1) | |

Circumradius | |

Dichoral angles | Sroh–8–girco: 135° |

Sroh–4–girco: 90° | |

Girco–6–girco: 60° | |

Related polytopes | |

Army | Srico |

Regiment | Srico |

Conjugate | Grand quasirhombic disicositetrachoron |

Convex core | Icositetrachoron |

Abstract properties | |

Euler characteristic | –96 |

Topological properties | |

Orientable | No |

Properties | |

Symmetry | F_{4}, order 1152 |

Convex | No |

Nature | Tame |

The **grand rhombic disicositetrachoron**, or **gardi**, is a nonconvex uniform polychoron that consists of 24 small rhombihexahedra and 24 great rhombicuboctahedra. Two small rhombihexahedra and four great rhombicuboctahedra join at each vertex.

It can be constructed as the blend of 3 small rhombiprismic tesseractihexadecachora, with the cubohemioctahedron cells blending out and the octagonal prisms blending into small rhombihexahedra.

## Vertex coordinates[edit | edit source]

The vertices are the same as those of the regiment colonel, the small rhombated icositetrachoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 6: Sphenoverts" (#155).