# Great rhombihexahedral prism

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Great rhombihexahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Grohp |

Elements | |

Cells | 12 cubes, 6 octagrammic prisms, 2 great rhombihexahedra |

Faces | 24+24+24 squares, 12 octagrams |

Edges | 24+48+48 |

Vertices | 48 |

Vertex figure | Butterfly pyramid, edge lengths √2, √2–√2, √2, √2–√2 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | |

Dichoral angles | Groh–4–cube: 90° |

Groh–8/3–stop: 90° | |

Cube–4–stop #1: 90° | |

Cube–4–stop #2: 45° | |

Height | 1 |

Number of external pieces | 200 |

Related polytopes | |

Army | Semi-uniform Ticcup, edge lengths (base), 1 (sides) |

Regiment | Goccope |

Dual | Great rhombihexacronic tegum |

Conjugate | Small rhombihexahedral prism |

Abstract & topological properties | |

Flag count | 1536 |

Euler characteristic | –8 |

Orientable | No |

Properties | |

Symmetry | B_{3}×A_{1}, order 96 |

Convex | No |

Nature | Tame |

The **great rhombihexahedral prism** or **grohp** is a prismatic uniform polychoron that consists of 2 great rhombihexahedra, 12 cubes, and 6 octagrammic prisms. Each vertex joins 1 great rhombihexahedron, 2 cubes, and 2 octagrammic prisms. As the name suggests, it is a prism based on the great rhombihexahedron.

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the great cubicuboctahedral prism.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 19: Prisms" (#934).

- Klitzing, Richard. "grohp".