Tetrahedral-hexagonal prismantiprismoid

The tetrahedral-hexagonal prismantiprismoid is a convex isogonal polyteron that consists of 6 tetrahedral prisms, 6 tetrahedral antiprisms, 6 digonal-hexagonal prismantiprismoids, and 24 tetrahedral wedges. 1 tetrahedral prism, 1 tetrahedral antiprism, 3 digonal-hexagonal prismantiprismoids, and 4 tetrahedral wedges join at each vertex. it can be obtained through the process of edge-alternating the dodecagonal-cubic duoprism so that the dodecagons become ditrigons. 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:
 * $$±\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac{\sqrt6-1}{4}, \frac{\sqrt2+\sqrt3}{4}\right),$$
 * $$±\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}, \frac{\sqrt2}{4},\,±\frac{1+\sqrt6}{4}, -\frac{\sqrt3-\sqrt2}{4}\right),$$
 * $$±\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac12, -\frac{\sqrt2}{2}\right).$$