First, the tetrahedron.

Next, the cube, with each square face augmented by a single rhombicosidodecahedron.

Next, this same operation is performed on an octahedron.

Next, the dodecahedron.

Finally, the last of the set, centered on an icosahedron. This one is my favorite.

I made these five models using Stella 4d: Polyhedron Navigator. You can try this program for free at http://www.software3d.com/Stella.php.