A three-dimensional (3D) dusty plasma crystalline with cubic configurations is considered. We calculate the interaction between particles up to distance √2a, implying the second-neighbor interactions for the simple cubic structure, the third-neighbor interactions for the body-centered cubic structure, and the forth-neighbor interactions the for face-centered cubic structure. Longitudinal and transverse dispersion relations are derived in arbitrary directions. The dispersion relations are studied in special directions, i.e. (1,0,0), (1, 1, 0)/√2, and (1, 1, 1)/√3. Study of dispersion relations with more neighbor interactions show that in some cases the results change physically.
