# Compound of three square antiprisms

Compound of three square antiprisms | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Gassic |

Elements | |

Components | 3 square antiprisms |

Faces | 24 triangles, 6 squares |

Edges | 24+24 |

Vertices | 24 |

Vertex figure | Isosceles trapezoid, edge length 1, 1, 1, √2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 3–3: |

4–3: | |

Central density | 3 |

Number of external pieces | 168 |

Level of complexity | 54 |

Related polytopes | |

Army | Non-uniform Snic, edge lengths (squares), (equilateral triangles), (between scalene triangles) |

Regiment | Gassic |

Dual | Compound of three square antitegums |

Conjugate | Compound of three square antiprisms |

Abstract & topological properties | |

Flag count | 192 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}+, order 24 |

Convex | No |

Nature | Tame |

The **great snub cube**, **gassic**, or **compound of three square antiprisms** is a uniform polyhedron compound. It consists of 24 triangles and 6 squares, with one square and three triangles joining at a vertex.

Its quotient prismatic equivalents are the small square gyroprismatic triothowedge, medial square gyroprismatic triorthowedge, great square gyroprismatic triorthowedge, small transitional square gyroprismatic triorthowedge, and great transitional square gyroprismatic triorthowedge, which are five-dimensional.

## Vertex coordinates[edit | edit source]

The vertices of a great snub cube of edge length 1 are given by all even sign changes and even permutations, plus all odd sign changes and odd permutations, of:

- .

## Related polyhedra[edit | edit source]

This compound is chiral. The compound of the two enantiomorphs is the great disnub cube.

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C8: Antiprismatics" (#46).

- Klitzing, Richard. "gassic".
- Wikipedia contributors. "Compound of three square antiprisms".