# Square retroprism

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Square retroprism | |
---|---|

Rank | 3 |

Type | Isogonal |

Space | Spherical |

Elements | |

Faces | 8 isosceles triangles, 2 squares |

Edges | 8+8 |

Vertices | 8 |

Vertex figure | Crossed isosceles trapezoid |

Related polytopes | |

Army | Squap |

Regiment | * |

Dual | Square concave antitegum |

Conjugate | Square antiprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

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

Convex | No |

Nature | Tame |

The **square retroprism**, also called the **square crossed antiprism**, is a prismatic isogonal polyhedron. It consists of 2 base squares and 8 isosceles triangles. Each vertex joins one square and three triangles. It is a crossed antiprism based on a square, seen as a 4/3-gon rather than 4/1. It cannot be made uniform.

It is isomorphic to the square antiprism.

## In vertex figures[edit | edit source]

A square retroprism with base edges of length 1 and side edges of length occurs as the vertex figure of the small distetracontoctachoron. One using side edges of length occurs as vertex figure of the quasiprismatotetracontoctachoron.

## Related polyhedra[edit | edit source]

There are an infinite amount of prismatic isogonal compounds that are the crossed antiprisms of compounds of squares.

## External links[edit | edit source]

- Klitzing, Richard. "n/d-ap".