Square duoantiprismatic antiprism

The square duoantiprismatic antiprism, or squiddapap, is a convex isogonal polyteron that consists of 2 square duoantiprisms, 16 digonal-square duoantiprisms, and 64 tetragonal disphenoidal pyramids. 1 square duoantiprism, 4 digonal-square duoantiprisms, and 5 tetragonal disphenoidal pyramids join at each vertex. It can be obtained through the process of alternating the octagonal duoprismatic prism. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{2+\sqrt2}{2}}$$ ≈ 1:1.30656.

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