We have studied possible ways of generating and growing the fullerenes having five-fold symmetry. Beginning with cyclopentane C5H10 and clusters C5C5, we obtained elementary fullerenes C10 and mini-fullerenes C20, and then we produced the fullerenes from C20 to C70, perfect (basic) and imperfect, as well as nanotubes. The basic fullerenes C20, C30, C40, C50, C60, and C70 have the ordinary five-fold symmetry, the intermediate ones having no such symmetry. Their imperfection is connected with extra 'interstitial' carbon dimers, the dimers playing the role of defects. One can define the imperfect fullerenes with defects as the fullerenes having topological five-fold symmetry. We have calculated the energies of both groups of fullerenes and discussed their dependence on a fullerene size and shape.