Digonal-pentagonal duoantiprism

The digonal-pentagonal duoantiprism or dipdap, also known as the 2-5 duoantiprism, is a convex isogonal polychoron that consists of 4 pentagonal antiprisms, 10 tetragonal disphenoids, and 20 digonal disphenoids. 2 pentagonal antiprisms,2 tetragonal disphenoids, and 4 digonal disphenoids join at each vertex. It can be obtained through the process of alternating the square-decagonal duoprism. However, it cannot be made uniform, as it generally has 3 edge lengths, which can be minimized to no fewer than 2 different sizes..

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.

Vertex coordinates
The vertices of a digonal-pentagonal duoantiprism, assuming that the pentagonal antiprisms are uniform of edge length 1, centered at the origin, are given by: with all even changes of sign except for the first coordinate, and with all odd changes of sign except for the first coordinate.
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,\sqrt{\frac{5+\sqrt5}{40}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,\sqrt{\frac{5+\sqrt5}{40}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac12,\,\sqrt{\frac{5+2\sqrt5}{20}},\,\sqrt{\frac{5+\sqrt5}{40}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$

An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, are given by: with all even changes of sign except for the first coordinate, and with all odd changes of sign except for the first coordinate.
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right),$$
 * $$\left(±\frac12,\,\sqrt{\frac{5+2\sqrt5}{20}},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right),$$