# Great cube

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Great cube | |
---|---|

Rank | 3 |

Type | Regular |

Space | Spherical |

Notation | |

Schläfli symbol | {4, 4/2} |

Elements | |

Components | 3 square dihedra |

Faces | 6 squares |

Edges | 12 |

Vertices | 6 doubled |

Vertex figure | Stellated square, edge length √2 |

Measures (edge length 1) | |

Circumradius | |

Volume | 0 |

Dihedral angle | 0° |

Central density | 3 |

Related polytopes | |

Army | Oct |

Regiment | Oct |

Dual | Stellated cube |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | B_{3}, order 48 |

Convex | No |

Nature | Tame |

The **great cube** or **compound of three square dihedra** is a degenerate regular polyhedron compound, being the compound of three square dihedra. It has 6 square faces and 6 fissary vertices.

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

When embedded in Euclidean 3-space all 6 of its faces pass through the center of the polyhedron.

## Vertex coordinates[edit | edit source]

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

- .