I am dealing with 2D lattices only. Some solutions to a PDE I am interested in consists of functions the minima of which organise themselves in an ordered periodic way: for instance they might arrange in a square lattice, or triangular lattice, or oblique with a given angle. The lattices might even be non-point lattices (but still periodic): example honeycomb or kagome lattice.
I was wondering whether it exists,given a periodic lattice, a transformation that can be done on the lattice which allows for the detection of the structure of the lattice or helps its classification. More specifically I was thinking whether one has in mind a clever way to use Fourier transforms or something of the sort to obtain a parameter which describes such lattices.
Otherwise any relevant reference on the topic? There must be someone studying these systems even though I could not find much in the literature.