I have the following question about triangulations (by non-intersecting diagonals, and edges) of regular polygons.
What is the number of triangulations of a regular n-gon, up to all symmetry (i.e. the whole dihedral group)?
For instance, if one discards symmetry, then the answer is the (n-2) Catalan number. If one only considers rotational symmetry, answer is given here.
The obvious approach is to apply Burnside/Polya, but I don't see a clear pattern on the cases that would show up for an arbitrary n.
I would like to know where to go from here.
Thanks!!