We report numerical investigations ora 3D model of diffusive growth of Fine particles, the internal structure of which corresponds to different crystal lattices. A growing cluster (particle) is immersed in and exchanges monomer building blocks with a surrounding medium of diffusing (off-lattice) monomers. On-surface dynamics of the latter is accounted for by allowing, in addition to detachment, monomer motion to the neighboring vacant crystal sites, according to probabilistic rules mimicking local thermalization. The key new feature of our model is the focus on the growth of a single cluster, emerging as a crystalline core, without development of defects that can control large-scale growth modes. This single, defect-free core growth is imposed by the specific dynamic rules assumed. Our results offer a possible explanation of the experimentally observed shape uniformity (i.e., fixed, approximately evenly sized proportions) in the synthesis of uniform colloids and nanoparticles. We demonstrate the basic principles of well-defined particle shape emergence in such growth, Specifically, several shapes are possible for a given crystal structure. The formation of shapes that follow the crystal symmetry and are uniform call be a result of the nonequilibrium nature of the growth process. The shape of a growing particle can be controlled by varying the relative rates of kinetic processes as well as by adjusting the concentration of monomers in the surrounding medium.