Given a 5-sided regular polyhedron, with labelled vertices, how would I label all of the symmetries in the form of a permutation?
I cannot find any similar problems to this, nor can I find an image of a 5-sided regular polyhedron. It seems as though such an object does not exist. How would I go about solving this?
My understanding is that a symmetry is a reflection along an axis such that the shape of the object does not change. How can I solve this problem without an image of the shape in question?
Is it merely the case that each symmetry is just the swapping of two vertices? I know that there are 10 such permutations.