Digonal-square duoantiprism

The digonal-square duoantiprism or disdap, also known as the 2-4 duoantiprism, is a convex isogonal polychoron that consists of 4 square antiprisms, 8 tetragonal disphenoids, and 16 digonal disphenoids. 2 square antiprisms, 2 tetragonal disphenoids, and 4 digonal disphenoids join at each vertex. It can be obtained through the process of alternating the square-octagonal 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:$$\sqrt{\frac{6+2\sqrt2}{7}}$$ ≈ 1:1.12303.

Vertex coordinates
The vertices of a digonal–square duoantiprism, assuming that the square antiprisms are uniform of edge length 1, centered at the origin, are given by:
 * $$\left(0,\,±\frac{\sqrt2}{2},\,\frac{\sqrt[4]{8}}{4},\,\frac{\sqrt[4]{8}}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt2}{2},\,-\frac{\sqrt[4]{8}}{4},\,-\frac{\sqrt[4]{8}}{4}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,\frac{\sqrt[4]{8}}{4},\,\frac{\sqrt[4]{8}}{4}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,-\frac{\sqrt[4]{8}}{4},\,-\frac{\sqrt[4]{8}}{4}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,\frac{\sqrt[4]{8}}{4},\,-\frac{\sqrt[4]{8}}{4}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,-\frac{\sqrt[4]{8}}{4},\,\frac{\sqrt[4]{8}}{4}\right).$$

An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, are given by:
 * $$\left(0,\,±\frac{\sqrt2}{2},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt2}{2},\,-\frac{\sqrt2}{4},\,-\frac{\sqrt2}{4}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,-\frac{\sqrt2}{4},\,-\frac{\sqrt2}{4}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,\frac{\sqrt2}{4},\,-\frac{\sqrt2}{4}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,-\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right).$$