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 a gyrochoron-symmetric subset of 10 vertices. The disphenoids are the decachoron's vertex figures, while the gyrobifastigium cells are subsymmetric facetings of the decachoron's truncated tetrahedron cells.

The ratio between the longest and shortest edges is 1:$$\sqrt3$$ ≈ 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)),