# Stellated cube

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Stellated cube | |
---|---|

Rank | 3 |

Type | Regular |

Space | Spherical |

Notation | |

Schläfli symbol | {4/2,4} |

Elements | |

Components | 3 square hosohedra |

Faces | 12 digons as 6 stellated squares |

Edges | 12 |

Vertices | 6 |

Vertex figure | Square, edge length 0 |

Measures (edge length 1) | |

Circumradius | |

Volume | 0 |

Dihedral angle | 90° |

Central density | 3 |

Related polytopes | |

Army | Oct |

Regiment | Stellated cube |

Dual | Great cube |

Abstract & topological properties | |

Schläfli type | {2,4} |

Orientable | Yes |

Properties | |

Symmetry | B_{3}, order 48 |

Convex | No |

Nature | Tame |

The **stellated cube** or **compound of three square hosohedra** is a degenerate regular polyhedron compound, being the compound of three square hosohedra. It has 12 digonal faces that form 6 stellated squares due to pairs falling in the same plane.

It can be formed as a degenerate stellation of the cube, by extending the edges to infinity.

Its quotient prismatic equivalent is the hexateron, which is five-dimensional.

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a stellated cube of edge length 1 centered at the origin are given by all permutations of:

- .