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 in the molecular version of this solid. Here is C320 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.