Small 10-3 double step prism

The small 10-3 double step prism is a convex isogonal polychoron that consists of 10 tetragonal disphenoids, 40 phyllic disphenoids of two kinds, and 40 irregular tetrahedra. 2 tetragonal disphenoids, 8 phyllic disphenoids, and 8 irregular tetrahedra join at each vertex. It 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 $$\frac{a}{b} = \frac{3-\sqrt5}{2}$$ would yield a biambodecachoron instead.

Vertex coordinates
Coordinates for the vertices of a small 10-3 double step prism are given by: where a/b is greater than $$\frac{3-\sqrt5}{2}$$ but less than 1, and k is an integer from 0 to 9.
 * $$\left(a\sin\left(\frac{2\pi k}{10}\right),\,a\cos\left(\frac{2\pi k}{10}\right),\,b\sin\left(\frac{6\pi k}{10}\right),\,b\cos\left(\frac{6\pi k}{10}\right)\right),$$
 * $$\left(b\sin\left(\frac{2\pi k}{10}\right),\,b\cos\left(\frac{2\pi k}{10}\right),\,a\sin\left(\frac{6\pi k}{10}\right),\,a\cos\left(\frac{6\pi k}{10}\right)\right),$$