Here’s the icosidodecahedron — one of the Archimedean solids.

Next, here’s what this solid looks like, if you augment each pentagonal face with a dodecahedron, and each triangular face with an icosahedron.

Finally, here’s what happens if you augment each pentagonal face of this second solid with an icosidodecahedron.

I used Stella 4d: Polyhedron Navigator to create these images. You can try this program, for free, at http://www.software3d.com/Stella.php.