Square duoantiprismatic antiprism

The square duoantiprismatic antiprism is a convex isogonal polyteron that consists of 2 square duoantiprisms, 16 digonal-square duoantiprisms and 64 tetragonal disphenoidal pyramids obtained through the process of alternating the octagonal duoprismatic prism. However, it cannot be made uniform.

Vertex coordinates
The vertices of a square duoantiprismatic antiprism, assuming that the edge length differences are minimized, centered at the origin, are given by:
 * (0, ±$\sqrt{2}$/2, 0, ±$\sqrt{2}$/2, $\sqrt{8|4}$/4),
 * (0, ±$\sqrt{2}$/2, ±$\sqrt{2}$/2, 0, $\sqrt{8|4}$/4),
 * (±$\sqrt{2}$/2, 0, 0, ±$\sqrt{2}$/2, $\sqrt{8|4}$/4),
 * (±$\sqrt{2}$/2, 0, ±$\sqrt{2}$/2, 0, $\sqrt{8|4}$/4),
 * (±1/2, ±1/2, ±1/2, ±1/2, $\sqrt{8|4}$/4),
 * (0, ±$\sqrt{2}$/2, ±1/2, ±1/2, -$\sqrt{8|4}$/4),
 * (±$\sqrt{2}$/2, 0, ±1/2, ±1/2, -$\sqrt{8|4}$/4),
 * (±1/2, ±1/2, 0, ±$\sqrt{2}$/2, -$\sqrt{8|4}$/4),
 * (±1/2, ±1/2, ±$\sqrt{2}$/2, 0, -$\sqrt{8|4}$/4).