Pentagonal-tetrahedral duoantiprism

The pentagonal-tetrahedral duoantiprism is a convex isogonal polyteron that consists of 10 tetrahedral antiprisms, 6 digonal-pentagonal duoantiprisms and 40 triangular scalenes obtained through the process of alternating the decagonal-cubic duoprism. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{20+2\sqrt5}{19}}$$ ≈ 1:1.13490.

Vertex coordinates
The vertices of a pentagonal-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, $\sqrt{50+10√5}$/10, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4),
 * (±(1+$\sqrt{5}$)/4, $\sqrt{50–10√5}$/20, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4),
 * (±1/2, –$\sqrt{25+10√5}$/10, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4),
 * (0, -$\sqrt{50+10√5}$/10, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4),
 * (±(1+$\sqrt{5}$)/4, -$\sqrt{50–10√5}$/20, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4),
 * (±1/2, $\sqrt{25+10√5}$/10, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4),