Transitional 10-3 double step prism

The transitional 10-3 double step prism is a convex isogonal polychoron that consists of 10 digonal scalenohedra, 20 phyllic disphenoids and 40 irregular tetrahedra. 3 digonal scalenohedra, 4 phyllic disphenoids, and 8 irregular tetrahedra join at each vertex. It can be obtained as the convex hull of two orthogonal 10-3 step prisms.

The ratio between the longest and shortest edges is 1:$$\sqrt5$$ ≈ 1:2.23607.

Vertex coordinates
Coordinates for the vertices of a transitional 10-3 double step prism are given by: where a = $\sqrt{42-18√5}$/6, b = $\sqrt{42+18√5}$/6 and k is an integer from 0 to 9.
 * (a*sin(2πk/10), a*cos(2πk/10), b*sin(6πk/10), b*cos(6πk/10)),
 * (b*sin(2πk/10), b*cos(2πk/10), a*sin(6πk/10), a*cos(6πk/10)),