We propose an ion trap configuration such that individual traps can be stacked together in a three dimensional simple cubic arrangement. The isolated trap as well as the extended array of ion traps are characterized for different locations in the lattice, illustrating the robustness of the lattice of traps concept. Ease in the addressing of ions at each lattice site, individually or simultaneously, makes this system naturally suitable for a number of experiments. Application of this trap to precision spectroscopy, quantum information processing and the study of few particle interacting system are discussed.