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 (a/b = (3-$\sqrt{5}$)/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.
 * (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)),