# Small rhombihexahedron

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Small rhombihexahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Sroh |

Elements | |

Faces | 12 squares, 6 octagons |

Edges | 24+24 |

Vertices | 24 |

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

Measures (edge length 1) | |

Circumradius | |

Dihedral angles | 8–4 #1: 90° |

8–4 #2: 45° | |

Central density | odd |

Number of external pieces | 66 |

Level of complexity | 10 |

Related polytopes | |

Army | Sirco |

Regiment | Sirco |

Dual | Small rhombihexacron |

Conjugate | Great rhombihexahedron |

Convex core | Cube |

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

It is a faceting of the small rhombicuboctahedron, using 12 of its squares, along with the 6 octagons of the small cubicuboctahedron.

It can be constructed as a blend of three orthogonal octagonal 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 rhombicuboctahedron.

## Related polyhedra[edit | edit source]

The rhombisnub hyperhombihedron is a uniform polyhedron compound composed of 5 small rhombihexahedra.

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#38).

- Klitzing, Richard. "sroh".
- Wikipedia contributors. "Small rhombihexahedron".
- McCooey, David. "Small Rhombihexahedron"