# Cuboctatruncated cuboctahedral prism

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Cuboctatruncated cuboctahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Cotcope |

Coxeter diagram | x x4/3x3x4*b () |

Elements | |

Cells | 8 hexagonal prisms, 6 octagonal prisms, 6 octagrammic prisms, 2 cuboctatruncated cuboctahedra |

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

Edges | 48+48+48+48 |

Vertices | 96 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | 10 |

Dichoral angles | Hip–4–stop: |

Cotco–8/3–stop: 90° | |

Cotco–6–hip: 90° | |

Cotco–8–op: 90° | |

Op–4–stop: 90° | |

Hip–4–op: | |

Height | 1 |

Central density | 4 |

Number of external pieces | 64 |

Related polytopes | |

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

Regiment | Cotcope |

Dual | Tetradyakis hexahedral tegum |

Conjugate | Cuboctatruncated cuboctahedral prism |

Abstract & topological properties | |

Flag count | 2304 |

Euler characteristic | –6 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×A_{1}, order 96 |

Convex | No |

Nature | Tame |

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

The cuboctatruncated cuboctahedral prism can be vertex-inscribed into the small skewverted prismatohexadecadisoctachoron and the antifrustary distetracontoctachoron.

## Cross-sections[edit | edit source]

## Vertex coordinates[edit | edit source]

The vertices of a cuboctatruncated 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" (#949).

- Klitzing, Richard. "cotcope".