On multiple connectedness of regions visible due to multiple diffuse reflections

It is known that the region V (s) of a simple polygon P , directly visible (illuminable) from an internal point s, is simply connected. Aronov et al. [2] established that the region V1(s) of a simple polygon visible from an internal point s due to at most one diffuse reflection on the boundary of the polygon P , is also simply connected. In this paper we establish that the region V2(s), visible from s due to at most two diffuse reflections may be multiply connected; we demonstrate the construction of an n-sided simple polygon with a point s inside it so that and the region of P visible from s after at most two diffuse reflections is multiple connected.