Square-tetrahedral duoantiprism

The square-tetrahedral duoantiprism, or squatetdap, is a convex isogonal polyteron that consists of 8 tetrahedral antiprisms, 6 digonal-square duoantiprisms, and 32 triangular scalenes. 2 tetrahedral antiprisms, 3 digonal-square duoantiprisms, and 5 triangular scalenes join at each vertex. It can be obtained through the process of alternating the octagonal-cubic duoprism. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{6+2\sqrt2}{7}}$$ ≈ 1:1.12303, occurring as the hull of 2 uniform square-tetrahedral duoprisms.

Vertex coordinates
The vertices of a square-tetrahedral duoantiprism, assuming that the edge length differences are minimized, centered at the origin, are given by: with all even changes of sign of the first three coordinates, and with all odd changes of sign of the first three coordinates.
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,0,\,±\frac{\sqrt2}{2}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac{\sqrt2}{2},\,0\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac12,\,±\frac12\right),$$