Kekule structures of fullerene C70

Despite that, besides Buckminsterfullerene C-60, fullerene C-70 is the next most stable structure, there are considerable differences in structural properties of these two most common fullereties. The paper reports on numerous mathematical properties of the set of Kekule structures of C-70. Of over 50,000 Kekule structures of fullerene C-70, only 2780 Kekule valence structures are distinct, while all the others are symmetry related. The subset of distinct Kekule valence structures was examined and classified into six classes according to the degree of freedom (df), varying from df = 5 to df = 11. Enumeration of conjugated circuits R-1, R-2 and R-3 points to two symmetry related dominant Kekule structures having the maximal number of 20 R-1. There are 16 distinct symmetry unrelated Kekule structures of C-70 that have no conjugated circuits R-1 at all.