Symmetry of hydrogenated C60

A graphical concept, which we call ‘spiral-like’ paths, is applied to the discussion of the point group symmetries of hydrogenated C60. It is established that the symmetry of a C60Hm isomer satisfies: (i) it is a subgroup of the Ih group of the parent molecule; (ii) for a subgroup with one or more symmetry planes, its order is a factor of 2m; (iii) for a subgroup without symmetry planes, its order is a factor of m. All the possible symmetries of C60Hm are readily tabulated.