The cluster below is formed by augmenting each face of the dodecahedron above with an icosidodecahedron.

Next, each triangular face is augmented with an icosahedron.

Now every pentagonal face is augmented with a dodecahedron.

Finally, the pentagonal faces in this cluster of polyhedra are augmented with icosidodecahedra. The resulting, new cluster has an overall icosahedral shape.

I did all of this using Stella 4d: Polyhedron Navigator. You can try this program for free at http://www.software3d.com/Stella.php.