In the study of pattern formation in symmetric physical systems a 3-dimensional structure in thin domains is often modelled as 2-dimensional one. As a contrast, in this work we use the full 3-dimensionality of the problem to give a theoretical interpretation and possibly decide whether the pattern seen in Reaction Diffusion systems naturally occur in either 2- or 3- dimension. For this purpose, we are concerned with functions in \(\mathbb{R}^{3}\) that are invariant under the action of a crystallographic group and the symmetries of their projections into a function defined on a plane.