Tetrahedral-hexagonal prismantiprismoid

The tetrahedral-hexagonal prismantiprismoid is a convex isogonal polyteron that consists of 4 tetrahedral prisms, 4 tetrahedral antiprisms, 6 digonal-square prismantiprismoids and 16 tetrahedral wedges obtained through the process of edge-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:$$\frac{2+2\sqrt6}{5}$$ ≈ 1:1.37980.

Vertex coordinates
The vertices of a tetrahedral-hexagonal prismantiprismoid, assuming that the edge length differences are minimized, centered at the origin, are given by all even sign changes of the first three coordinates of:
 * ±($\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, ±($\sqrt{6}$-1)/4, $\sqrt{5+2√6}$/4),
 * ±($\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, ±(1+$\sqrt{6}$)/4, -$\sqrt{5-2√6}$/4),
 * ±($\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, ±1/2, -$\sqrt{2}$/2).