# Square ditetragoltriate

Square ditetragoltriate | |
---|---|

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Notation | |

Bowers style acronym | Squiddet |

Elements | |

Cells | 16 rectangular trapezoprisms, 8 square prisms |

Faces | 32 isosceles trapezoids, 32 rectangles, 8 squares |

Edges | 16+32+32 |

Vertices | 32 |

Vertex figure | Notch |

Measures (based on variant with trapezoids with 3 unit edges) | |

Edge lengths | Edges of smaller square (32): 1 |

Lacing edges (16): 1 | |

Edges of larger square (32): 2 | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Squiddet |

Regiment | Squiddet |

Dual | Square tetrambitriate |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{2}≀S_{2}, order 128 |

Convex | Yes |

Nature | Tame |

The **square ditetragoltriate** or **squiddet**, also known as the **8-3 quadruple step prism** or **digonal truncatoprismantiprismoid**, is a convex isogonal polychoron and the second member of the ditetragoltriate family. It consists of 8 square prisms and 16 rectangular trapezoprisms. 2 square prisms and 4 rectangular trapezoprisms join at each vertex. However, it cannot be made uniform. It is the first in an infinite family of isogonal square prismatic swirlchora.

This polychoron can be alternated into a digonal double antiprismoid, which is also nonuniform.

It can be obtained as the convex hull of 2 similarly oriented semi-uniform square duoprisms, one with a larger xy square and the other with a larger zw square.

It can also be constructed as a partial faceting of the truncated hexadecachoron.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:2. This value is also the ratio between the two sides of the two semi-uniform duoprisms.

The skeleton of this polytope is isomorphic to that of the 5-cube.

## Vertex coordinates[edit | edit source]

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