Here’s an icosahedron.

Here is is again, with prisms attached to each face. The prisms are 2.1 times as long as the triangle-edges.

This is a Stewart G3.

The final step is to attach these Stewart G3s to the ends of the long prisms shown above.

I think I’ll stop there. All these polyhedron-manipulations were performed using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.