Rotary polygons in configurations (Q540131)

Summary: A polygon \(A\) in a configuration \(\mathcal C\) is called rotary if \(\mathcal C\) admits an automorphism which acts upon \(A\) as a one-step rotation. We study rotary polygons and their orbits under the group of automorphisms (and antimorphisms) of \(\mathcal C\). We determine the number of such orbits for several symmetry types of rotary polygons in the case when \(\mathcal C\) is flag-transitive. As an example, we provide tables of flag-transitive \((v_3)\) and \((v_4)\) configurations of small order containing information on the number and symmetry types of corresponding rotary polygons.