Are there finite examples of metachirality? My intuition says no, because I can't even think of finite examples with glide symmetry or screw symmetry, both of which feel like a weaker thing to ask for. I also suspect that any example of metachirality must in some way rely on translation, and if I can somehow formalise and prove that notion, I think I'll be done. (Because I know that translational invariance implies that, at least in one direction, the object is infinite )
In the positive case, I am looking for examples of finite symmetry groups (so maybe the object to consider is infinite, but the symmetry group is somehow still finite), but examples with finite objects would be cool too.
In the negative case, are there any proofs that all examples of metachirality need to be finite? And do such proofs have anything to say about glide/screw symmetries?