Rotational level structure is investigated for a number of lower symmetry fullerene structures including the Buckyball isotopomer C-13 C-12(59), and it is compared to that of C-12(60) using quantum mechanical and semiclassical theory. Rotational spectra of C-13 C-12(59) differs markedly from that of icosahedrally symmetric Buckyball because the presence of a single additional neutron completely breaks its rotational symmetry from I-h for C-60 down to a single C-s reflection plane for C-13 C-12(59). Nevertheless, most rotational energy levels remain surprisingly clustered and well ordered. Predictions are made for types of spectroscopic structure resulting from reduction of icosahedral symmetry to C-s, C-2 upsilon, C-3 upsilon, and C-5 upsilon such as might be encountered in intrahedrally doped XC(59). Semiclassical techniques help to label the spectra of molecules undergoing such extreme symmetry breaking and to explain why high J levels still maintain so much order and degeneracy under these conditions. These techniques may also be useful toward understanding the dynamics of hindered rotors in solution or solid fullerite, as well as in the interpretation of high resolution gas phase spectra of fullerene molecules or ions.