Great square double tetraswirlprism

The great square double tetraswirlprism is an isogonal polychoron with 32 square gyroprisms, 192 rhombic disphenoids of three kinds, 128 phyllic disphenoids, and 256 irregular tetrahedra. 2 square gyroprisms, 6 rhombic disphenoids, 4 phyllic disphenoids, and 8 irregular tetrahedra join at each vertex. It is the fourth in an infinite family of isogonal square prismatic swirlchora, the others being the small square double tetraswirlprism and transitional square double tetraswirlprism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{8+2\sqrt2+4\sqrt{2+\sqrt2}}}{2}$$ ≈ 1:2.13421.

Vertex coordinates
Coordinates for the vertices of a great square double tetraswirlprism optimized via the ratio method, centered at the origin, are given by, along with their 90°, 180° and 270° rotations in the xy axis of: where a = $\sqrt{2-√2-√2}$/2, b = $\sqrt{2+√2-√2}$/2 and k is an integer from 0 to 7.
 * ±(a*sin(kπ/8), a*cos(kπ/8), b*cos(kπ/8), b*sin(kπ/8)),
 * ±(b*sin(kπ/8), b*cos(kπ/8), a*cos(kπ/8), a*sin(kπ/8)),