Digonal-triangular tetraswirlprism

The digonal-triangular tetraswirlprism is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 8 triangular gyroprisms, 12 rhombic disphenoids, and 72 phyllic disphenoids of three kinds. 2 triangular gyroprisms, 2 rhombic disphenoids, and 12 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the octagonal-dodecagonal duoprism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{18351060+6695112\sqrt3+60498\sqrt{44354+25312\sqrt3}}}{3361}$$ ≈ 1:2.05950.

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 triangle T 1 and digon D 2 with length ratio 1:1:
 * T 1 × D 2,
 * T 3 × D 4 (T 1 rotated 30 degrees and D 2 rotated 45 degrees),
 * T 5 × D 6 (T 1 rotated 60 degrees and D 2 rotated 90 degrees),
 * T 7 × D 8 (T 1 rotated 90 degrees and D 2 rotated 135 degrees).