Can someone please explain to me the symmetry of a pentagon in relation to the dihedral group, having both rotational and reflective symmetry. I understand this is in relation to a regular polygon but I don't understand it in plain english.

I'm very interested in applying symmetrical principals to irregular pentagons, specifically irregular five pointed stars.

How would I mathematically choose an outer point that would best divide irregular pentagrams symmetrically once a line is drawn from the outer point to the opposite vertex in the middle pentagon?

Area, angles, both?

Any help is appreciated.