Transitional triangular double triswirlprism

The transitional triangular double triswirlprism is a convex isogonal polychoron that consists of 18 triangular gyroprisms, 54 tetragonal antiwedges, and 27 rhombic disphenoids. 2 triangular gyroprisms, 6 tetragonal antiwedges, and 2 rhombic disphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal triangular-triangular triswirlprisms based on triangles of different edge length. However, it cannot be made uniform. It is the third in an infinite family of isogonal triangular prismatic swirlchora, the others being the small triangular double triswirlprism and great triangular double triswirlprism.

The ratio between the longest and shortest edges is 1:$$\sqrt6\cos\frac\pi9$$ ≈ 1:2.30177.

Vertex coordinates
Coordinates for the vertices of a transitional triangular double triswirlprism are given as Cartesian products of the vertices of two triangles T 1 and T 2 with length ratio 1:$$\frac{2+\sec\frac\pi9}{2}$$ ≈ 1:1.53209:
 * T 1 × T 2,
 * T 3 × T 4 (T 1 and T 2 both rotated 40 degrees),
 * T 5 × T 6 (T 1 and T 2 both rotated 80 degrees),
 * T 2 × T 1,
 * T 4 × T 3,
 * T 6 × T 5.