Transitional square double triswirlprism

The transitional square double triswirlprism is a convex isogonal polychoron that consists of 24 square gyroprisms, 96 tetragonal antiwedges, and 48 tetragonal disphenoids. 2 square gyroprisms, 6 tetragonal antiwedges, and 2 tetragonal disphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal square-square triswirlprisms based on squares of different edge length. However, it cannot be made uniform. It is the third in an infinite family of isogonal square prismatic swirlchora, the others being the small square double triswirlprism and great square double triswirlprism.

The ratio between the longest and shortest edges is 1:$$\frac{1+\sqrt3}{2}$$ ≈ 1:1.36603.

Vertex coordinates
Coordinates for the vertices of a transitional square double triswirlprism are given as Cartesian products of the vertices of two triangles T 1 and T 2 with length ratio 1:$$\sqrt3$$ ≈ 1:1.73205:
 * S 1 × S 2,
 * S 3 × S 4 (S 1 and S 2 both rotated 30 degrees),
 * S 5 × S 6 (S 1 and S 2 both rotated 60 degrees),
 * S 2 × S 1,
 * S 4 × S 3,
 * S 6 × S 5.