# Blended cube

Blended cube | |
---|---|

Rank | 3 |

Space | Spherical, 4-dimensional space |

Notation | |

Schläfli symbol | |

Elements | |

Faces | 6 skew squares |

Edges | 12 |

Vertices | 8 |

Related polytopes | |

Army | Hexadecachoron |

Halving | Tetrahedron |

Abstract & topological properties | |

Euler characteristic | 2 |

Schläfli type | {4,3} |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | (A_{3}×2×A_{1})/2, order 48 |

Convex | No |

The **blended cube** or **skew cube** is a regular skew polyhedron in 4D Euclidean space. It can be constructed by taking a cube and skewing it in the 4th dimension. It is the blend of a cube and the digon. Since the cube is 2-colorable it is abstractly equivalent to the cube. The cube is the only planar regular polyhedron that has this property, although the square tiling and hexagonal tiling are also 2-colorable and thus also have abstractly equivalent blends.

## Vertex coordinates[edit | edit source]

For a skew cube with edge length 1 and skew distance its vertex coordinates can be given by

- ,

where the total number of negative coordinates is odd.

The vertex coordinates of a skew cube with skew distance and edge length 1 can be given by all permutations of:

- ,
- .

These correspond to the vertices of a hexadecachoron with unit edge length.

## Gallery[edit | edit source]

A net.

## Related polytopes[edit | edit source]

The blended cube has the same faces and vertex figure as the blended Petrial tetrahedron, and the two are abstractly equivalent.