Anisotropic surface diffusion and strain are used to explain the formation of three-dimensional (In,Ga)As quantum dot lattices. The diffusion characteristics of the surface coupled with the elastic anisotropy of the matrix, provides an excellent opportunity to influence the dot positions. In particular, quantum dots that are laterally organized into long chains or chessboard two-dimensional arrays vertically organized with strict vertical ordering or vertical ordering that is inclined to the sample surface normal are accurately predicted and observed.