Digonal-square tetraswirlprism

The digonal-square tetraswirlprism, also known as the 16-2 double step prism or 16-6 double step prism, is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 8 square antiprisms, 16 rhombic disphenoids, and 96 phyllic disphenoids of three kinds. 2 square antiprisms, 2 rhombic disphenoids, and 12 phyllic disphenoids joined at each vertex. It can be obtained as a subsymmetrical faceting of the octagonal-hexadecagonal duoprism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{14356+6402\sqrt2+388\sqrt{1186+833\sqrt2}}}{97}$$ ≈ 1:2.11968.

Vertex coordinates
Coordinates for the vertices of a digonal-square tetraswirlprism, assuming that the edge length differences are minimized, are given as Cartesian products of the vertices of square S 1 and digon D 2 with length ratio 1:1:
 * S 1 × D 2,
 * S 3 × D 4 (S 1 rotated 22.5 degrees and D 2 rotated 45 degrees),
 * S 5 × D 6 (S 1 rotated 45 degrees and D 2 rotated 90 degrees),
 * S 7 × D 8 (S 1 rotated 67.5 degrees and D 2 rotated 135 degrees).