# Octahemioctahedral prism

The **octahemioctahedral prism** or **ohope** is a prismatic uniform polychoron that consists of 2 octahemioctahedra, 8 triangular prisms, and 4 hexagonal prisms. Each vertex joins 1 octahemioctahedron, 2 triangular prisms, and 2 hexagonal prisms. As the name suggests, it is a prism based on the octahemioctahedron.

Octahemioctahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Ohope |

Coxeter diagram | x x3/2o3x3*b () |

Elements | |

Cells | 8 triangular prisms, 4 hexagonal prisms, 2 octahemioctahedra |

Faces | 16 triangles, 24 squares, 8 hexagons |

Edges | 12+48 |

Vertices | 24 |

Vertex figure | Bowtie pyramid, edge lengths 1, √3 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | 0 |

Dichoral angles | Oho–3–trip: 90° |

Oho–6–hip: 90° | |

Trip–4–hip: | |

Height | 1 |

Central density | 0 |

Number of external pieces | 48 |

Related polytopes | |

Army | Cope |

Regiment | Cope |

Dual | Octahemioctacronic bipyramid |

Conjugate | None |

Abstract & topological properties | |

Flag count | 768 |

Euler characteristic | –2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×A_{1}, order 96 |

Convex | No |

Nature | Tame |

## Vertex coordinates edit

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

## External links edit

- Bowers, Jonathan. "Category 19: Prisms" (#909).

- Klitzing, Richard. "ohope".