# Snub square antiprism

Snub square antiprism | |
---|---|

Rank | 3 |

Type | CRF |

Notation | |

Bowers style acronym | Snisquap |

Elements | |

Faces | 8+16 triangles, 2 squares |

Edges | 8+8+8+16 |

Vertices | 8+8 |

Vertex figures | 8 mirror-symmetric pentagons, edge length 1, 1, 1, 1, √2 |

8 pentagons, edge length 1 | |

Measures (edge length 1) | |

Volume | ≈ 3.60122 |

Central density | 1 |

Number of external pieces | 26 |

Level of complexity | 10 |

Related polytopes | |

Army | Snisquap |

Regiment | Snisquap |

Dual | Tetraoctapentagonal hexadecahedron |

Conjugate | Retrosnub square antiprism |

Abstract & topological properties | |

Flag count | 160 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | (I_{2}(8)×A_{1})/2, order 16 |

Convex | Yes |

Nature | Tame |

The **snub square antiprism** is one of the 92 Johnson solids (J_{85}). It consists of 8+16 triangles and 2 squares.

It can be constructed from a square antiprism by expanding the two halves outward and inserting a set of 16 triangles in between the halves.

## Coordinates[edit | edit source]

Coordinates for a snub square antiprism with unit edge length are given by

- (±1/2, ±1/2,
*C*/2), - (±√2A/2, 0,
*B*/2), - (0, ±√2A/2,
*B*/2), - (±A/2, ±A/2, −
*B*/2), - (0, ±√2/2, −
*C*/2), - (±√2/2, 0, −
*C*/2),

where *A* is the second-to-greatest root of

and where *B* and *C* are given by

From these coordinates, its volume can be calculated as *ξ* ≈ 3.60122, where *ξ* is the greatest real root of

^{[1]}

## Related polyhedra[edit | edit source]

The snub square antiprism can be considered to be the square case in the family of snub antiprisms. The snub triangular antiprism is the regular icosahedron, and the snub disphenoid or snub digonal antiprism is another Johnson solid. No other members of this family can be made convex and regular-faced (the snub pentagonal antiprism can be made with regular faces, but is concave).

## External links[edit | edit source]

- Klitzing, Richard. "snisquap".
- Quickfur. "The Snub Square Antiprism".

- Wikipedia contributors. "Snub square antiprism".
- McCooey, David. "Snub Square Antiprism"