Triangular tetraswirlprism

The triangular tetraswirlprism is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 24 triangular antiprisms, 36 rhombic disphenoids, and 72 phyllic disphenoids. 4 triangular gyroprisms, 4 rhombic disphenoids, and 8 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the dodecagonal duoprism. It is the fourth in an infinite family of isogonal triangular dihedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\frac{3+\sqrt3}{2}$$ ≈ 1:2.36603.

Vertex coordinates
Coordinates for the vertices of a triangular tetraswirlprism constructed as the convex hull of four triangular duoprisms of edge length 1, are given as Cartesian products of the vertices of triangle T 1:
 * T 1 × T 1,
 * T 2 × T 2 (T 1 rotated 30 degrees),
 * T 3 × T 3 (T 1 rotated 60 degrees).
 * T 4 × T 4 (T 1 rotated 90 degrees).