# Quasirhombicuboctahedral prism

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Quasirhombicuboctahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Quercope |

Coxeter diagram | x x4/3o3x () |

Elements | |

Cells | 8 triangular prisms, 6+12 cubes, 2 quasirhombicuboctahedra |

Faces | 16 triangles, 12+24+24+24 squares |

Edges | 24+48+48 |

Vertices | 48 |

Vertex figure | Crossed isosceles trapezoidal pyramid, edge lengths 1, √2, √2, √2 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Querco–4–cube: 90° |

Querco–3–trip: 90° | |

Cube–4–cube: 45° | |

Trip–4–cube: | |

Height | 1 |

Central density | 5 |

Number of external pieces | 490 |

Related polytopes | |

Army | Semi-uniform Ticcup, edge lengths (base), 1 (sides) |

Regiment | Goccope |

Dual | Great deltoidal icositetrahedral tegum |

Conjugate | Small rhombicuboctahedral prism |

Abstract & topological properties | |

Flag count | 1536 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×A_{1}, order 96 |

Convex | No |

Nature | Tame |

The **quasirhombicuboctahedral prism** or **quercope** is a prismatic uniform polychoron that consists of 2 quasirhombicuboctahedra, 6+12 cubes, and 8 triangular prisms. Each vertex joins 1 quasirhombicuboctahedron, 1 triangular prism, and 3 cubes. As the name suggests, it is a prism based on the quasirhombicuboctahedron.

## Cross-sections[edit | edit source]

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Category 19: Prisms" (#933).

- Klitzing, Richard. "quercope".