# Small cubicuboctahedral prism

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Small cubicuboctahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Soccope |

Coxeter diagram | x x4/3o3x4*b () |

Elements | |

Cells | 8 triangular prisms, 6 cubes, 6 octagonal prisms, 2 small cubicuboctahedra |

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

Edges | 24+48+48 |

Vertices | 48 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Socco–4–cube: 90° |

Socco–3–trip: 90° | |

Socco–8–op: 90° | |

Cube–4–op: 90° | |

Trip–4–op: | |

Height | 1 |

Central density | 2 |

Number of pieces | 80 |

Related polytopes | |

Army | Sircope |

Regiment | Sircope |

Dual | Small hexacronic icositetrahedral tegum |

Conjugate | Great cubicuboctahedral prism |

Abstract properties | |

Euler characteristic | –6 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×A_{1}, order 96 |

Convex | No |

Nature | Tame |

The **small cubicuboctahedral prism** or **soccope** is a prismatic uniform polychoron that consists of 2 small cubicuboctahedra, 6 cubes, 8 triangular prisms, and 6 octagonal prisms. Each vertex joins 1 small cubicuboctahedron, 1 triangular prism, 1 cube, and 2 octagonal prisms. As the name suggests, it is a prism based on the small cubicuboctahedron.

## Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the small rhombicuboctahedral prism.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 19: Prisms" (#924).

- Klitzing, Richard. "soccope".