Great 10-3 double step prism

The great 10-3 double step prism is a convex isogonal polychoron that consists of 10 tetragonal disphenoids, 20 phyllic disphenoids, and 80 irregular tetrahedra of two kinds. 2 tetragonal disphenoids, 4 phyllic disphenoids, and 16 irregular tetrahedra join at each vertex. I t can be obtained as one of several polychora formed as the convex hull of two orthogonal 10-3 step prisms.

This polychoron cannot be optimized using the ratio method, because the solution (a/b = (3-$\sqrt{5}$)/2) would yield a biambodecachoron instead.

Vertex coordinates
Coordinates for the vertices of a great 10-3 double step prism are given by: where a/b is greater than $$\frac{7-3\sqrt5}{2}$$ but less than $$\frac{3-\sqrt5}{2}$$ 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)),