Pentagonal-tetrahedral duoantiprism

The pentagonal-tetrahedral duoantiprism, or petetdap, is a convex isogonal polyteron that consists of 10 tetrahedral antiprisms, 6 digonal-pentagonal duoantiprisms, and 40 triangular scalenes. 2 tetrahedral antiprisms, 3 digonal-pentagonal duoantiprisms, and 5 triangular scalenes join at each vertex. It can be obtained through the process of alternating the decagonal-cubic duoprism. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{20+2\sqrt5}{19}}$$ ≈ 1:1.13490, which occurs as the hull of 2 uniform pentagonal-tetrahedral duoprisms.

Vertex coordinates
The vertices of a pentagonal-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.
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,0,\,\sqrt{\frac{5+\sqrt5}{10}}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,0,\,-\sqrt{\frac{5+\sqrt5}{10}}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac{1+\sqrt5}{4},\,-\sqrt{\frac{5-\sqrt5}{40}}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,±\frac12,\,\sqrt{\frac{5+2\sqrt5}{20}}\right),$$