The self-organization of pyramidal PbSe islands that spontaneously form during strained-layer epitaxial growth of PbSe/Pb1-x Eux Te (x = 0.05 to 0.1) super-lattices results in the formation of three-dimensional quantum-dot crystals. In these crystals, the dots are arranged in a trigonal lattice with a face-centered cubic (fcc)-like A-B-C-A-B-C vertical stacking sequence. The lattice constant of the dot crystal can be tuned continuously by changing the superlattice period. As shown by theoretical calculations, the elastic anisotropy in these artificial dot crystals acts in a manner similar to that of the directed chemical bonds of crystalline solids. The narrow size distribution and excellent control of the dot arrangement may be advantageous for optoelectronic device applications.