# Square duotruncatoprism

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Square duotruncatoprism | |
---|---|

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Notation | |

Bowers style acronym | Squidtep |

Elements | |

Cells | 16 tetragonal disphenoids, 32 wedges, 16 rectangular trapezoprisms, 8 ditetragonal prisms |

Faces | 64 isosceles triangles, 64 isosceles trapezoids, 32+32 rectangles, 8 ditetragons |

Edges | 32+32+64+64 |

Vertices | 64 |

Vertex figure | Mirror-symmetric bi-apiculated tetrahedron |

Measures (based on octagon edge length 1 and same radius ratio as uniform-derived square duoexpandoprism) | |

Edge lengths | Edges of octagons (32+32): 1 |

Lacing edges (64): | |

Edges of pseudo-squares (64): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Squidtep |

Regiment | Squidtep |

Dual | Square duotruncatotegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{2}≀S_{2}, order 128 |

Convex | Yes |

Nature | Tame |

The **square duotruncatoprism** or **squidtep** is a convex isogonal polychoron and the third member of the duotruncatoprism family. It consists of 8 ditetragonal prisms, 16 rectangular trapezoprisms, 32 wedges, and 16 tetragonal disphenoids. 2 ditetragonal prisms, 2 rectangular trapezoprisms, 3 wedges, and 1 tetragonal disphenoid join at each vertex. It can be obtained as the convex hull of two orthogonal semi-uniform square-ditetragonal duoprisms whose ditetragonal prism cells have a smaller circumradius than their square prisms. Although it cannot be made uniform while remaining convex, it is isomorphic to the inverted quasiprismatodishexadecachoron.