Square double gyroantiprismoid

The square double gyroantiprismoid is a convex isogonal polychoron and the third member of the double gyroantiprismoids that consists of 16 square antiprisms, 32 tetragonal disphenoids, 64 rhombic disphenoids and 128 sphenoids. However, it cannot be made uniform. It is the second in an infinite family of isogonal square prismatic swirlchora.

Vertex coordinates
Coordinates for the vertices of a square double gyroantiprismoid, assuming that the square antiprisms are regular of edge length 1, centered at the origin, are given by:
 * (0, ±$\sqrt{2}$/2, 0, ±$\sqrt{2+2√2}$/2),
 * (0, ±$\sqrt{2}$/2, ±$\sqrt{2+2√2}$/2, 0),
 * (±$\sqrt{2}$/2, 0, 0, ±$\sqrt{2+2√2}$/2),
 * (±$\sqrt{2}$/2, 0, ±$\sqrt{2+2√2}$/2, 0),
 * (0, ±$\sqrt{2+2√2}$/2, 0, ±$\sqrt{2}$/2),
 * (0, ±$\sqrt{2+2√2}$/2, ±$\sqrt{2}$/2, 0),
 * (±$\sqrt{2+2√2}$/2, 0, 0, ±$\sqrt{2}$/2),
 * (±$\sqrt{2+2√2}$/2, 0, ±$\sqrt{2}$/2, 0),
 * (±1/2, ±1/2, ±$\sqrt{1+√2}$/2, ±$\sqrt{1+√2}$/2),
 * (±$\sqrt{1+√2}$/2, ±$\sqrt{1+√2}$/2, ±1/2, ±1/2).