We present a characterization of fullerenes based on 12 x12 matrices which register separations between all twelve pentagonal faces in fullerenes. Some properties of such matrices (eigenvalues, the characteristic polynomial and sequences based on distance distributions) are illustrated. It is shown that derived invariants can serve for classification and characterization of not only different fullerene isomers but also for characterization of pentagonal faces in individual fullerenes.
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Milan Randić (1994) studied this question.
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