# Great rhombihexahedron

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Great rhombihexahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Groh |

Elements | |

Faces | 12 squares, 6 octagrams |

Edges | 24+24 |

Vertices | 24 |

Vertex figure | Butterfly, edge lengths √2 and √2–√2 |

Measures (edge length 1) | |

Circumradius | |

Dihedral angles | 8/3–4 #1: 90° |

8/3–4 #2: 45° | |

Central density | odd |

Number of external pieces | 366 |

Level of complexity | 56 |

Related polytopes | |

Army | Tic, edge length |

Regiment | Gocco |

Dual | Great rhombihexacron |

Conjugate | Small rhombihexahedron |

Convex core | Rhombic dodecahedron |

Abstract & topological properties | |

Flag count | 192 |

Euler characteristic | -6 |

Orientable | No |

Genus | 8 |

Properties | |

Symmetry | B_{3}, order 48 |

Flag orbits | 4 |

Convex | No |

Nature | Tame |

The **great rhombihexahedron**, or **groh**, is a uniform polyhedron. It consists of 12 squares and 6 octagrams. Two squares and two octagrams meet at each vertex. It also has 8 triangular pseudofaces and 6 square pseudofaces.

It is a faceting of the great cubicuboctahedron, using its 6 octagrams along with 12 squares of the quasirhombicuboctahedron.

It can be constructed as a blend of three orthogonal octagrammic prisms, with 6 pairs of coinciding square faces blending out.

## Vertex coordinates[edit | edit source]

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

## Related polyhedra[edit | edit source]

The rhombisnub quasihyperhombihedron is a uniform polyhedron compound composed of 5 great rhombihexahedra.

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#47).

- Klitzing, Richard. "groh".
- Wikipedia contributors. "Great rhombihexahedron".
- McCooey, David. "Great Rhombihexahedron"