I have a board game, such as tic-tac-toe, played on a square. How many different board positions look unique, but are actually the exact same if you just rotate the board or flip the pieces across some axis? What about for games played on other (non-square) regular polygons?
I've used Google and the search on Math Stack Exchange to research this, but haven't come up with useful results. Most of them talk about symmetry, but without any formulas.
This link states the amount of symmetry lines is equal to the number or sides/vertices of a regular polygon, which may help solve the problem.
I realize now that one of the reasons for this may be that it's such a simple problem, but I still feel like it's useful to have a record of the question and see what answers come of it - surely someone else will like a simple answer to this question later on.