We present a general comprehensive framework for the description of symmetries of complex light fields, facilitating the construction of sophisticated periodic structures carrying phase dislocations. In particular, we demonstrate the derivation of all three fundamental two-dimensional vortex lattices based on vortices of triangular, quadratic, and hexagonal shape, respectively. We show that these patterns represent the foundation of complex three-dimensional lattices with outstanding helical intensity distributions which suggest valuable applications in holographic lithography. This systematic approach is substantiated by a comparative study of corresponding numerically calculated and experimentally realized complex intensity and phase distributions.

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