Within the geometric optics approximation, the phase functions of randomly oriented ice crystals are calculated as a series relative to multiplicity of internal collisions of light inside the particles. In the case of convex crystals, it is shown that the coefficients of the series provide the most information about the crystal shapes, while the angular functions of this series are weakly dependent on the shapes. The prevailing role of the term corresponding to one internal collision is emphasized. Three numbers describing a distribution of the single-collision scattered light among the aureole and halos of 22 degrees and 46 degrees prove to be the basic parameters by which to characterize scattering by hexagonal ice crystals.