Triangular-square triswirlprism

The triangular-square triswirlprism is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 9 square antiprisms, 12 triangular antiprisms, and 72 phyllic disphenoids of two kinds. 2 square antiprisms, 2 triangular antiprisms, and 8 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the enneagonal-dodecagonal duoprism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{6}{10-3\sqrt3-4\cos\frac{2\pi}{9}}}$$ ≈ 1:1.85713.

Vertex coordinates
Coordinates for the vertices of a triangular-square triswirlprism, assuming that the edge length differences are minimized, are given as Cartesian products of the vertices of square S 1 and triangle T 2 with length ratio 1:1:
 * S 1 × T 2,
 * S 3 × T 4 (S 1 rotated 30 degrees and T 2 rotated 40 degrees),
 * S 5 × T 6 (S 1 rotated 60 degrees and T 2 rotated 80 degrees).