# Cubohemioctahedron

Cubohemioctahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Cho |

Coxeter diagram | (o4/3x3x4*a)/2 ()/2 |

Elements | |

Faces | 6 squares, 4 hexagons |

Edges | 24 |

Vertices | 12 |

Vertex figure | Bowtie, edge lengths √2 and √3 |

Measures (edge length 1) | |

Circumradius | 1 |

Dihedral angle | |

Number of pieces | 30 |

Level of complexity | 4 |

Related polytopes | |

Army | Co |

Regiment | Co |

Dual | Hexahemioctacron |

Conjugate | None |

Abstract properties | |

Euler characteristic | –2 |

Topological properties | |

Orientable | No |

Genus | 5 |

Properties | |

Symmetry | B_{3}, order 48 |

Convex | No |

Nature | Tame |

The **cubohemioctahedron**, or **cho**, is a quasiregular polyhedron and one of 10 uniform hemipolyhedra. It consists of 6 squares and 4 "hemi" hexagons, passing through its center, with two of each joining at a vertex. It also has 8 triangular pseudofaces. Its square faces are parallel to those of a cube, and its hemi hexagonal faces are parallel to those of an octahedron: hence the name. It can be derived as a rectified petrial octahedron.

The visible portion of this solid resembles a cuboctahedron with eight tetrahedra carved out. In fact the square faces are the same ones as those of the cuboctahedron, while the hexagons are its equatorial planes.

It is uniform under both cubic and tetrahedral symmetry. In fact it occurs far more often with tetrahedral symmetry in higher uniform polytopes.

## Vertex coordinates[edit | edit source]

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

## Related polyhedra[edit | edit source]

The great antirhombicosahedron is a uniform polyhedron compound composed of 5 cubohemioctahedra.

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 3: Quasiregulars" (#23).

- Bowers, Jonathan. "Batch 1: Oct and Co Facetings" (#3 under co).

- Klitzing, Richard. "cho".

- Wikipedia Contributors. "Cubohemioctahedron".
- McCooey, David. "Cubohemioctahedron"