Hexagonal-tetrahedral duoantiprism

The hexagonal-tetrahedral duoantiprism is a convex isogonal polyteron that consists of 12 tetrahedral antiprisms, 6 digonal-hexagonal duoantiprisms and 48 triangular scalenes obtained through the process of alternating the dodecagonal-cubic duoprism. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{10+4\sqrt3}{13}}$$ ≈ 1:1.14113.

Vertex coordinates
The vertices of a hexagonal-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, ±1, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4),
 * (±$\sqrt{3}$/2, ±1/2, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4),
 * (±1, 0, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4),
 * (±1/2, ±$\sqrt{3}$/2, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4),