# Compound of two cubes

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Compound of two cubes | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Coxeter diagram | xo4ox xx |

Elements | |

Components | 2 cubes |

Faces | 8 squares, 4 squares as 2 stellated octagons |

Edges | 8+16 |

Vertices | 16 |

Vertex figure | Equilateral triangle, edge length √2 |

Measures (edge length 1) | |

Circumradius | |

Volume | 2 |

Dihedral angle | 90° |

Height | 1 |

Central density | 2 |

Number of external pieces | 18 |

Level of complexity | 6 |

Related polytopes | |

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

Regiment | * |

Dual | Compound of two octahedra |

Conjugate | Compound of two cubes |

Abstract & topological properties | |

Flag count | 96 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(8)×A_{1}, order 32 |

Convex | No |

Nature | Tame |

The **stellated octagonal prism** or **compound of two cubes** is a prismatic uniform polyhedron compound. It consists of 2 stellated octagons and 8 squares. Each vertex joins one stellated octagon and two squares. As the name suggests, it is a prism based on a stellated octagon.

Its quotient prismatic equivalent is the square antiprismatic prism, which is four-dimensional.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a stellated octagonal prism of edge length 1 centered at the origin are given by:

## Variations[edit | edit source]

This compound has variants where the bases are non-regular compounds of two squares. In these cases the compound has only square prismatic symmetry and the convex hull is a ditetragonal prism.