Periodic system of fullerenes from the mathematical standpoint

The types of classification for fullerenes’ property are considered. It accumulates empirically found the horizontal and vertical symmetry of fullerenes which give a preliminary classification. Two different symmetries are united into a common symmetry producing the periodic system of fullerenes. This system may be considered as the topological lattice in the topological space of the points corresponding to the fullerenes. The system gives the general classification of fullerenes on the basis of symmetry. © A.I. Melker, M.A. Krupina, 2024.