I'm writing a program and need a way to identify and enumerate the number of possible distinct crystallographic domains when depositing one 2D lattice on top of another.

I've posed this as a question in Math SE: Number of possible rotational domains of one 2D lattice on top of another? but possibly because I lack the proper "math words" it might not be receiving views by the users who can answer it. I'm sure it's a solved problem.


  1. Would this question be on-topic here if suitably rewritten for this site?
  2. If so, might it be likely to receive an answer?

Snippet from the linked question:

Square and hexagonal lattices shown at 0, 30 and 60 degrees:

square and hexagonal lattices shown at 0, 30 and 60 degrees

Square and hexagonal lattices shown at +/-10 degrees:

square and hexagonal lattices shown at +/-10 degrees

  • 2
    $\begingroup$ I don't understand what do you mean by absolute angle. $\endgroup$
    – nicoguaro Mod
    Mar 3, 2020 at 18:45
  • $\begingroup$ @nicoguaro Thanks, I probably need to work on that. I think you're referring to "a given angle who's absolute value is $\theta$" in the linked question. In the description of the problem above that I say "If I ask for an offset of 10 degrees then there are two ways (+/- 10°)." You are right there are more clearer ways to say what I'm trying to describe, I'll think about it. I mention crystallographic domains in the question, and those are regions that are geometrically distinct but have the same energy. $\endgroup$
    – uhoh
    Mar 3, 2020 at 23:33
  • $\begingroup$ For two hexagonal lattices of the lowest symmetry group the +10 and -10 degree orientations would have the same energy. That's the kind of thing I'm getting at, but I'm still having trouble expressing this. I appreciate the input. $\endgroup$
    – uhoh
    Mar 3, 2020 at 23:34
  • 1
    $\begingroup$ It seems that the problem you describe is something that can be either computed exactly or estimated numerically. We don’t get very many questions regarding computational abstract algebra/group theory so it may not get the attention you seek as posed. Try to reframe it as a computational geometry question if possible. You may also want to break it into several smaller questions that build to answer your question. Ex. How can i detect rotational symmetry on a discrete lattice numerically? $\endgroup$
    – Paul Mod
    Mar 4, 2020 at 5:51
  • $\begingroup$ @Paul I see what you mean, thanks! $\endgroup$
    – uhoh
    Mar 4, 2020 at 5:53


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