# Square duotruncatoalterprism

Jump to navigation
Jump to search

Square duotruncatoalterprism | |
---|---|

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Elements | |

Cells | 16 tetragonal disphenoids, 16 rectangular trapezoprisms, 16 square cupolas, 8 square prisms |

Faces | 64 isosceles triangles, 64 isosceles trapezoids, 32 rectangles, 16 squares, 8 ditetragons |

Edges | 32+32+64+64 |

Vertices | 64 |

Vertex figure | Monoaugmented isosceles trapezoidal pyramid |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Square duotruncatoaltertegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{2}≀S_{2}, order 128 |

Convex | Yes |

Nature | Tame |

The **square duotruncatoalterprism** is a convex isogonal polychoron and the third member of the duotruncatoalterprism family. It consists of 8 square prisms, 16 square cupolas, 16 rectangular trapezoprisms, and 16 tetragonal disphenoids. 1 square prism, 3 square cupolas, 2 rectangular trapezoprisms, and 1 tetragonal disphenoid 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 cannot be optimized using the ratio method, because the solution (with intended minimal ratio 1:2) would yield a square duotransitionalterprism instead.