Figure 4.

(A) The spiral algorithm was used to try every possible permutation of 12 pentagons for each given number of hexagons. The fraction of permutations that yields closed polyhedra decreases rapidly with increasing number of hexagons or (as shown) of vertices. (B) Notwithstanding, the number of possible closed fullerenes increases dramatically with increasing size (vertex number) in a combinatorial fashion. Fit: Fullerenes = 4.093 × 10⁻¹⁴ × vertices^9.416.