Transitional square double tetraswirlprism

The transitional square double tetraswirlprism is an isogonal polychoron with 32 square gyroprisms, 64 rectangular gyroprisms, and 64 rhombic disphenoids. 2 square gyroprisms, 4 rectangular gyroprisms, and 2 rhombic disphenoids 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 great square double tetraswirlprism.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{544+187\sqrt2+34\sqrt{274+193\sqrt2}}}{17}$$ ≈ 1:2.35559.

Vertex coordinates
Coordinates for the vertices of a transitional square double tetraswirlprism, centered at the origin, are given by, along with their 90°, 180° and 270° rotations in the xy axis of: where a = $\sqrt{544-102√2-68√26-7√2}$/34, b = $\sqrt{612+102√2+68√26-7√2}$/34 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)),