Hexagonal-tetrahedral duoantiprism

The hexagonal-tetrahedral duoantiprism, or hatetdap, is a convex isogonal polyteron that consists of 12 tetrahedral antiprisms, 6 digonal-hexagonal duoantiprisms, and 48 triangular scalenes. 2 tetrahedral antiprisms, 3 digonal-hexagonal duoantiprisms, and 5 triangular scalenes join at each vertex. It can be 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. This occurs as the hull of 2 uniform hexagonal-tetrahedral duoprisms.

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 first three coordinates, and with all odd changes of sign of the first three coordinates.
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,0,\,±1\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac{\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±1,\,0\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac12,\,±\frac{\sqrt3}{2}\right),$$