The growth of fullerene nanocrystals, composed of only C-60, only C-70, or a mixture of both fullerenes, has been investigated by scanning tunneling microscopy (STM). The nanocrystals, formed on a NaCl ultrathin layer partially covering a Au(111) surface, have characteristic truncated-triangular or hexagonal shapes, with lateral size up to 100 nm and a typical height of two to four molecular layers. This growth mode differs considerably from the ones observed on metallic surfaces. STM images with bias-dependent submolecular resolution reveal the spatial distribution of the electronic density originating from the molecular orbitals. A comparison of the experimental results with first-principles density functional theory calculations allows us to unambiguously determine the orientation and the nature of individual fullerene molecules in the surface layer of the nanocrystals.