Triangular double triswirlprism

The triangular double triswirlprism is a convex isogonal polychoron that consists of 18 triangular gyroprisms, 27 rhombic disphenoids, 108 phyllic disphenoids of two kinds, and 108 irregular tetrahedra. 2 triangular gyroprisms, 2 rhombic disphenoids, 8 phyllic disphenoids, and 8 irregular tetrahedra 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.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{8+2\cos\frac\pi9+\sec\frac\pi9}}{2}$$ ≈ 1:1.65405.

Vertex coordinates
Coordinates for the vertices of a triangular double triswirlprism, assuming that the edge length differences are minimized, are given as Cartesian products of the vertices of two triangles T 1 and T 2 with length ratio 1:$$2\cos\frac\pi9$$ ≈ 1:1.87939: Another set of coordinates for a triangular double triswirlprism, assuming that the ratio method is used, are given as Cartesian products of the vertices of two triangles T 1 and T 2 with length ratio 1:$$1+\frac{2}{\cot\frac\pi9-1}$$ ≈ 1:2.14451:
 * 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.
 * 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.