There was a period of time in which my post above was not registering and so I posted it again. Both copies eventually made it to the web archives, which I thought was redundant, so I edited this copy to be something new.
I just got 'Divided Spheres: Geodesics and the Orderly Subdivision of the Sphere' by Edward S. Popko. Some links to pix follow at the end.
This book just came out and was stacked up at 'Bridges' I hear. That's the math - art bridges conference, this year in Baltimore. My associate David Koski was there, and he has been feeding me some reports.
Since art is being eliminated from many curricula, art teachers sent packing, I think it behooves the math curriculum to re-create these bridges to art. They may be computationally intensive, like Mandelbrot and Mandelbulb, or not.
Popko's book talks a lot about Waterman Polyhedra. I'm the guy who named them that, so Steve Waterman wouldn't have to (looks less vain when someone else names your chief discovery after you). Gerald de Jong, myself, and a few others, helped get those computed and rendered originally. Waterman himself was using Excel and physical modeling.
Waterman found quite a few collaborators over the years, as the polyhedra were /are somewhat stunning. Find the convex hull defined by all CCP balls distance x from a center CCP ball. Other balls of lesser distance than x will still be part of this set. I used qhull (free open source: qhull.org) in my own modeling.