Square trioantiprism

The square trioantiprism, or squittap, is a convex isogonal polypeton that consists of 24 square duoantiprismatic antiprisms and 256 digonal trisphenoids. 6 of each facet type join at each vertex. It can be obtained through the process of alternating the octagonal trioprism. However, it cannot be made uniform.

The ratio between the longest and shortest edges is 1:$$\sqrt{\frac{2+\sqrt2}{2}}$$ ≈ 1:1.30656.

Vertex coordinates
The vertices of a square trioantiprism, based on squares of edge length 1, centered at the origin, are given by:
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(0,\,±\frac{\sqrt2}{2},\,0,\,±\frac{\sqrt2}{2},\,±\frac12,\,±\frac12\right),$$
 * $$\left(0,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,0,\,±\frac{\sqrt2}{2},\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,±\frac{\sqrt2}{2},\,0,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac12,\,0,\,±\frac{\sqrt2}{2},\,0,\,±\frac{\sqrt2}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,0,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt2}{2},\,0,\,0,\,±\frac{\sqrt2}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt2}{2},\,0,\,±\frac{\sqrt2}{2},\,0\right),$$
 * $$\left(0,\,±\frac{\sqrt2}{2},\,±\frac12,\,±\frac12,\,0,\,±\frac{\sqrt2}{2}\right),$$
 * $$\left(0,\,±\frac{\sqrt2}{2},\,±\frac12,\,±\frac12,\,±\frac{\sqrt2}{2},\,0\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,±\frac12,\,±\frac12,\,0,\,±\frac{\sqrt2}{2}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,±\frac12,\,±\frac12,\,±\frac{\sqrt2}{2},\,0\right).$$