Square-tetrahedral duoantiprism

The square-tetrahedral duoantiprism is a convex isogonal polyteron that consists of 8 tetrahedral antiprisms, 6 digonal-square duoantiprisms and 32 triangular scalenes 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.

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.
 * ($\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, 0, ±$\sqrt{2}$/2),
 * ($\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, ±$\sqrt{2}$/2, 0),
 * ($\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, ±1/2, ±1/2),