Transitional 10-3 double gyrostep prism

The transitional 10-3 double gyrostep prism is a convex isogonal polychoron that consists of 10 chiral gyrobifastigia and 10 tetragonal disphenoids. 2 gyrobifastigia and 4 tetraognal disphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal stretched 10-3 step prisms.

It can also be constructed as a subsymmetrical faceting of the decachoron, formed by removing 10 vertices.

The ratio between the longest and shortest edges is 1:$\sqrt{3}$ ≈ 1:1.73205.

Vertex coordinates
Coordinates for the vertices of a transitional 10-3 double gyrostep prism are given by: where a = $$\sqrt{\frac{5-2\sqrt5}{5}}$$, b = $$\sqrt{\frac{5+2\sqrt5}{5}}$$, 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)),