# Small rhombihexahedral prism

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

Small rhombihexahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Srohp |

Elements | |

Cells | 12 cubes, 6 octagonal prisms, 2 small rhombihexahedra |

Faces | 24+24+24 squares, 12 octagons |

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 | Sroh–4–cube: 90° |

Sroh–8–op: 90° | |

Cube–4–op #1: 90° | |

Cube–4–op #2: 45° | |

Height | 1 |

Number of external pieces | 92 |

Related polytopes | |

Army | Sircope |

Regiment | Sircope |

Dual | Small rhombihexacronic tegum |

Conjugate | Great rhombihexahedral prism |

Abstract & topological properties | |

Euler characteristic | –8 |

Orientable | No |

Properties | |

Symmetry | B_{3}×A_{1}, order 96 |

Convex | No |

Nature | Tame |

Its vertex figure matches that of the chasmic cuboctachoron; while the equilateral triangles still correspond to cubes, the butterfly and isosceles triangles now correspond to the blend of 2 octagonal prisms' vertex figures.

## Vertex coordinatesEdit

Its vertices are the same as those of its regiment colonel, the small rhombicuboctahedral prism.

## External linksEdit

- Bowers, Jonathan. "Category 19: Prisms" (#925).