Octagonal ditetragoltriate

The octagonal ditetragoltriate or odet is a convex isogonal polychoron and the sixth member of the ditetragoltriate family. It consists of 16 octagonal prisms and 64 rectangular trapezoprisms. 2 octagonal 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 octagonal prismatic swirlchora.

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

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

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{2+\sqrt{4-2\sqrt2}}{2}$$ ≈ 1:1.54120. This value is also the ratio between the two squares of the two semi-uniform duoprisms.

Vertex coordinates
The vertices of an octagonal ditetragoltriate, assuming that the trapezoids have three equal edges of length 1, centered at the origin, are given by:
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}{2},\,±\frac{2+\sqrt{4-2\sqrt2}}{4},\,±\frac{2+2\sqrt2+\sqrt{4+2\sqrt2}}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}{2},\,±\frac{2+2\sqrt2+\sqrt{4+2\sqrt2}}{4},\,±\frac{2+\sqrt{4-2\sqrt2}}{4}\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac{2+\sqrt{4-2\sqrt2}}{4},\,±\frac{2+2\sqrt2+\sqrt{4+2\sqrt2}}{4}\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac{2+2\sqrt2+\sqrt{4+2\sqrt2}}{4},\,±\frac{2+\sqrt{4-2\sqrt2}}{4}\right),$$
 * $$\left(±\frac{2+\sqrt{4-2\sqrt2}}{4},\,±\frac{2+2\sqrt2+\sqrt{4+2\sqrt2}}{4},\,±\frac12,\,±\frac{1+\sqrt2}{2}\right),$$
 * $$\left(±\frac{2+\sqrt{4-2\sqrt2}}{4},\,±\frac{2+2\sqrt2+\sqrt{4+2\sqrt2}}{4},\,±\frac{1+\sqrt2}{2},\,±\frac12\right),$$
 * $$\left(±\frac{2+2\sqrt2+\sqrt{4+2\sqrt2}}{4},\,±\frac{2+\sqrt{4-2\sqrt2}}{4},\,±\frac12,\,±\frac{1+\sqrt2}{2}\right),$$
 * $$\left(±\frac{2+2\sqrt2+\sqrt{4+2\sqrt2}}{4},\,±\frac{2+\sqrt{4-2\sqrt2}}{4},\,±\frac{1+\sqrt2}{2},\,±\frac12\right).$$