# Square duotransitionalterprism

Square duotransitionalterprism | |
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File:Square duotransitionalterprism.png | |

Rank | 4 |

Type | Isogonal |

Elements | |

Cells | 16 rectangular trapezoprisms, 8 square prisms, 8 square trapezorhombihedra |

Faces | 64 isosceles trapezoids, 32 rectangles, 16+16 squares |

Edges | 32+64+64 |

Vertices | 64 |

Vertex figure | Isosceles trapezoidal pyramid |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Square duotransitionaltertegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{2}≀S_{2}, order 128 |

Convex | Yes |

Nature | Tame |

The **square duotransitionalterprism** is a convex isogonal polychoron and the third member of the duotransitionalterprism family. It consists of 8 square trapezorhombihedra, 8 square prisms, and 16 rectangular trapezoprisms. 2 square trapezorhombihedra, 1 square prism, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal square-ditetragonal duoprisms. However, it cannot be made scaliform.

This polychoron can be alternated into a digonal duotransitionalterantiprism, which is also not scaliform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:2.

## Vertex coordinates[edit | edit source]

The vertices of a square duotransitionalterprism, assuming that the isosceles trapezoids have three equal edges of length 1, centered at the origin, are given by:

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