Nested polygons, such as the pentagram, have been of interest from ancient times. Other well known examples are the Fano triangle and the Grunbaum double octagon. A family of double polygons proved to be of special interest in the quest for slope minimal point configurations.
For any polygon additional polygons can be constructed from intersections of sides and diagonals. The number of possible polgyons from interesections depends on the number of vertices and how many numbers are relatively prime to the number of vertices.
My current interest in automorphisms of pluripolygons that preserve parallelism as a subset of slope preserving automorphisms of point configurations.
Following are three examples.
Those interested in this topic can contact either Mark Fitch.