Periodic system of fullerenes: the column of six-fold symmetry

The possible ways of generation and growing the fullerenes having six-fold symmetry have been studied. Beginning with cyclohexane C₆H₁₂, benzol C₆H₆ and clusters C₆C₆, we obtained elementary fullerenes C₁₂ and mini-fullerenes C₂₄, which produce the fullerenes from C₂₄ to C₈₄; perfect (basic), as well as nanotubes. The basic fullerenes C₂₄, C₃₆, C₄₈, C₆₀, C₇₂ and C₈₄ have the ordinary six-fold symmetry. We have calculated their energies and discussed possible reasons for their dependence on a fullerene size and shape in the framework of the periodic system of fullerenes.