# Quasitruncated cuboctahedral prism

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Quasitruncated cuboctahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Quitcope |

Coxeter diagram | x x4/3x3x () |

Elements | |

Cells | 12 cubes, 8 hexagonal prisms, 6 octagrammic prisms, 2 quasitruncated cuboctahedra |

Faces | 24+24+24+24 squares, 16 hexagons, 12 octagrams |

Edges | 48+48+48+48 |

Vertices | 96 |

Vertex figure | Irregular tetrahedron, edge lengths √2, √3, √2–√2 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Cube–4–stop: 135° |

Quitco–8/3–stop: 90° | |

Quitco–6–hip: 90° | |

Quitco–4–cube: 90° | |

Hip–4–stop: | |

Cube–4–hip: | |

Height | 1 |

Central density | -1 |

Number of external pieces | 150 |

Related polytopes | |

Army | Semi-uniform Gircope, edge lengths (octagons), (remaining base edges), 1 (sides) |

Regiment | Quitcope |

Dual | Great disdyakis dodecahedral tegum |

Conjugate | Great rhombicuboctahedral prism |

Abstract & topological properties | |

Flag count | 2304 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×A_{1}, order 96 |

Convex | No |

Nature | Tame |

The **quasitruncated cuboctahedral prism**, or **quitcope**, is a prismatic uniform polychoron that consists of 2 quasitruncated cuboctahedra, 6 octagrammic prisms, 8 hexagonal prisms, and 12 cubes. Each vertex joins one of each type of cell. As the name suggests, it is a prism based on the quasitruncated cuboctahedron.

The quasitruncated cuboctahedral prism can be vertex-inscribed into the great cubihexadecadisoctachoron.

## Vertex coordinates[edit | edit source]

The vertices of a quasitruncated cuboctahedral prism of edge length 1 are given by all permutations of the first three coordinates of:

## External links[edit | edit source]

- Bowers, Jonathan. "Category 19: Prisms" (#946).

- Klitzing, Richard. "quitcope".