Triangular-tetrahedral duoantiprism

The triangular-tetrahedral duoantiprism, or tratetdap, is a convex isogonal polyteron that consists of 6 tetrahedral antiprisms, 6 digonal-triangular duoantiprisms, and 24 triangular scalenes. 3 tetrahedral antiprisms, 2 digonal-triangular duoantiprisms, and 5 triangular scalenes join at each vertex. It can be obtained through the process of alternating the hexagonal-cubic duoprism. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{30}}{5}$$ ≈ 1:1.09545. This occurs when it is a hull of 2 uniform triangular-tetrahedral duoprisms.

Vertex coordinates
The vertices of a triangular-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.
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,0,\,\frac{\sqrt3}{3}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac12,\,-\frac{\sqrt3}{6}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,0,\,-\frac{\sqrt3}{3}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac12,\,\frac{\sqrt3}{6}\right).$$