The duals of the geodesic domes are polyhedra with hexagonal and pentagonal faces. This particular one has 320 vertices, with those vertices representing carbon atoms. Here is C-320 as a polyhedron.
The next image shows this molecule as a ball-and-stick model.
Finally, here it is as a space-filling molecular model.
All three images were created with Stella 4d: Polyhedron Navigator. This is the page to visit if you want to try Stella for yourself: http://www.software3d.com/Stella.php.