# Quasirhombicuboctahedron

Quasirhombicuboctahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Querco |

Coxeter diagram | x4/3o3x () |

Elements | |

Faces | 8 triangles, 6+12 squares |

Edges | 24+24 |

Vertices | 24 |

Vertex figure | Crossed isosceles trapezoid, edge lengths 1, √2, √2, √2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 4–4: 45° |

4–3: | |

Central density | 5 |

Number of external pieces | 488 |

Level of complexity | 73 |

Related polytopes | |

Army | Tic, edge length |

Regiment | Gocco |

Dual | Great deltoidal icositetrahedron |

Conjugate | Small rhombicuboctahedron |

Convex core | Chamfered cube |

Abstract & topological properties | |

Flag count | 192 |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | B_{3}, order 48 |

Flag orbits | 4 |

Convex | No |

Nature | Tame |

The **quasirhombicuboctahedron**, also commonly known as the **nonconvex great rhombicuboctahedron**, or **querco** is a uniform polyhedron. It consists of 8 triangles and 6+12 squares, with one triangle and three squares meeting at each vertex. It also has 6 octagrammic pseudofaces. It can be obtained by quasicantellation of the cube or octahedron, or equivalently by pushing either polyhedron's faces inward and filling the gaps with squares.

6 of the squares in this figure have full B_{2} symmetry, while 12 of them have only A_{1}×A_{1} symmetry with respect to the whole polyhedron.

It is also sometimes called a **great rhombicuboctahedron**, but is not to be confused with the convex polyhedron with the same name.

It is a faceting of the great cubicuboctahedron, using the original's squares and triangles, while also introducing 12 additional squares.

## Related polyhedra[edit | edit source]

The rhombisnub quasirhombicosicosahedron is a uniform polyhedron compound composed of 5 quasirhombicuboctahedra.

The quasirhombicuboctahedron can be constructed as an octagrammic prism augmented with retrograde square cupolas facing inwards on the octagrammic faces.

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#46).

- Bowers, Jonathan. "Batch 5: Sirco and gocco Facetings" (#2 under gocco).

- Klitzing, Richard. "querco".
- Wikipedia contributors. "Nonconvex great rhombicuboctahedron".
- McCooey, David. "Uniform Great Rhombicuboctahedron"