I'm looking for a table or database containing mathematical functions that belong to crystallographic space groups by having the same symmetry elements.

Imagine a 2D square planar lattice. It has a 4-fold rotational symmetry as well as 4 reflection directions. The function $f(x,y) = \cos(x) + \cos(y)$ has the same symmetry. What I'm looking for is a database / table which contains such functions for (ideally all) crystallographic space groups (I'm currently most interested in Bi2Se3 and thus the space group #166)

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    $\begingroup$ +1. I love this question, largely because I love databases. I'm looking forward to seeing the answers that arise here. $\endgroup$ Commented Apr 10, 2023 at 17:24
  • $\begingroup$ I do not know anything about such databases, though my intuition says that's a problem for evolutionary programming. All you need is a carefully prepared set of symmetry operations for your system (symops for the space group of interest and symops for supergroups), and a code for creating/modifying functions and symmetry checking. $\endgroup$ Commented Apr 11, 2023 at 2:55
  • $\begingroup$ Mika, @IvanChernyshov, I was just looking through a book by Schoenflies from 1891 and found something that might be interesting in the context of this conversation. $\endgroup$ Commented Oct 13, 2023 at 20:57


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