Triangular-tetrahedral duoantiprism

The triangular-tetrahedral duoantiprism is a convex isogonal polyteron that consists of 6 tetrahedral antiprisms, 6 digonal-triangular duoantiprisms and 24 triangular scalenes obtained through the process of alternating the hexagonal-cubic duoprism. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{30}}{5}$$ ≈ 1:1.09545.

Vertex coordinates
The vertices of a triangular-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 last three coordinates, and with all odd changes of sign of the last three coordinates.
 * (0, $\sqrt{3}$/3, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4),
 * (±1/2, -$\sqrt{3}$/6, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4),
 * (0, -$\sqrt{3}$/3, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4),
 * (±1/2, $\sqrt{3}$/6, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4).