Density functional calculations accurately reproduce the known bond lengths for C60F18, shown recently (single crystal X-ray structure) to possess a fully aromatic hexagonal ring, and they correctly predict the planarity of this ring. Isostructural C60H18 is also calculated to have an aromatic benzenoid hexagonal ring, and to be marginally less planar. The four benzenoid hexagonal rings of T symmetry C60H36 and C60F36, and the three benzenoid rings of C3 symmetry C60H36 and C60F36 are predicted to be aromatic, with both the T symmetry and the fluorinated species again having the slightly shorter bond lengths and the greater planarity; by these measures T-C60F36 is as aromatic as C60F18. In another C3v isomer of C60H18, which had been predicted (AM1) to be thermodynamically more stable than the known isomer, density functional calculations show the central benzenoid ring to have slightly greater bond alternation, greater bond lengths, to be less planar and the molecule to be overall less stable than the known isomer; this is attributed to the greater strain in the three adjacent pentagonal rings. Sites for ether formation are conjectured based on the recent finding that oxygen inserts into long FC–CF bonds of fluorofullerenes.