The smallest fullerene is the dodecahedral C 20 . There are no fullerenes with 22 vertices.  The number of fullerenes C 2n grows with increasing n = 12, 13, 14, ..., roughly in proportion to n 9 (sequence A007894 in the OEIS ). For instance, there are 1812 non-isomorphic fullerenes C 60 . Note that only one form of C 60 , the buckminsterfullerene alias truncated icosahedron , has no pair of adjacent pentagons (the smallest such fullerene). To further illustrate the growth, there are 214,127,713 non-isomorphic fullerenes C 200 , 15,655,672 of which have no adjacent pentagons. Optimized structures of many fullerene isomers are published and listed on the web. 
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S. Roberson, A. Sehgal, A. Fahey, A. Karim. “Time-of-flight secondary ion mass spetrometry (TOF-SIMS) for high-throughput characterization of biosurfaces.” Applied Surface Science 9375. Elsevier Science . (2002) 1-4.