rwg>n 2 3 4 6 10 [intersecting cylinders] F 4 12 24 40 60 84 112 144 180 [cylindrical faces on intersection] rwg>A 180-hedron! Is there any limit to the number of congruent faces
on a ["ball shaped"] polyhedron?
The ten great circles on the in-sphere of the intersection of ten cylinders through opposite pairs of faces of an icosahedron form twelve pentagrams arranged dodecahedrally tip-to-tip, the interstices being 20 nonregular hexagons, each enclosed by three pentagrams. The quadrilateral Voronoi regions for the 60 segments separating pentagons from their triangular "arms" are definitely smaller than those for the 120 segments separating those triangles from hexagons. ASIMOV! I WANT MY MONEY BACK! Well, maybe not. If you unite each hexagon with three nonconsecutive neighbor triangles, you get equilateral triangles enclosing the pentagons in an appealing camera-shutter arrangement that maybe we could sell to a soccer ball manufacturer.
Of course, my original question was about "ball shaped" polyhedra, if we can make that precise. I think I can do 216.
I haven't a clue what I was thinking here, so http://img114.exs.cx/img114/9895/bunny8ts.jpg --rwg THRENODIC CHONDRITE (Nine letters isn't much, but it's unusual to have no common digrams.)