You have an unlimited supply of regular polygons, each with side length 1: triangles, squares, pentagons, etc. Some combinations of these polygons may be arranged in a “cycle” so that they all share a common vertex and any consecutive pair of polygons share exactly a common edge. (See the example below.) What is the largest n-gon in such a cycle?
Hint (sort of): There is a much better title for this post, but unfortunately it would give away the solution to the problem.