[Karthik]

Originally Posted by sanddrag

I wouldn't mind seeing a pic of the inside, and what all those screws attach to.

Same. Just using a bit of combinatorial geometry, my guess is that what you'll find is a webbing that is essentially the dual graph¹ of the of soccer ball. Since a soccer ball (or Buckyball mathematically speaking) is a polyhedron of pentagonal and hexagonal faces with vertices of degree 3, the resulting dual will be a polyhedron with only triangular faces, with vertices of degree 5 and 6. These vertices look to be the insertion points of the screws.

All that being said, the webbing might be constructed differently than the perfect dual graph to allow for easier assembly and construction. Alas, what is perfect and elegant in the mathematical world, rarely works in the real world.

1. In graph theory, a dual graph of a given graph G is a graph which has a vertex for each plane region of G, and an edge for each edge in G joining two neighboring regions. This theory can be extending into 3D polyhedra geometry.