Square ditetragoltriate

Square ditetragoltriate
(OFF file)
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	$\frac{\sqrt{10}}{2} ≈ 1.58114$
Central density	1
Related polytopes
Army	Squiddet
Regiment	Squiddet
Dual	Square tetrambitriate
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B2≀S2, 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

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

• $\left(±\frac12,\,±\frac12,\,±1,\,±1\right),$
• $\left(±1,\,±1,\,±\frac12,\,±\frac12\right).$