Digonal-square triswirlprism

The digonal-square triswirlprism, also known as the 12-2 double step prism or 12-4 double step prism, is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 6 square antiprisms, 12 rhombic disphenoids, and 48 phyllic disphenoids of two kinds. 2 square antiprisms, 2 rhombic disphenoids, and 8 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the hexagonal-dodecagonal duoprism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{260+104\sqrt3}}{13}$$ ≈ 1:1.61380.

Vertex coordinates
Coordinates for the vertices of a digonal-square triswirlprism, 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 (T 1 rotated 30 degrees and D 2 rotated 60 degrees),
 * S 5 × D 6 (T 1 rotated 60 degrees and D 2 rotated 120 degrees).