These two polyhedra are the icosahedron (left), and the great icosahedron (right).
Since the faces of both of these polyhedra are equilateral triangles, it is possible to augment each of the icosahedron’s twenty faces with a great icosahedron. Here is the result.
I used Stella 4d to make these images. You may try this program for yourself at http://www.software3d.com/Stella.php.