Geometric methods for the construction of three structural motifs, the icosahedron, Ino's decahedron, and the complete octahedron, are proposed. On the basis of the constructed lattices and the genetic algorithm, a method for optimization of large size Lennard-Jones (LJ) clusters is presented. Initially, the proposed method is validated by optimization of LJ(13-309) Clusters with the above structural motifs. Results show that the proposed rnethod successfully located all the lowest known minima with an excellent performance; for example, based on Ino's decahedron with 147 lattice sites, the mean time consumed for successful optirnization of LJ(75) is only 0.61 s (Pentium III, 1 GHz), and the percentage Success is 100%. Then, putative global minima of LJ(310-561) clusters are predicted with the method. By theoretical analysis, these global minima are reasonable, although further verification or proof is still needed.