If on a circumference they are marked $n$ equally spaced points, those points can be joined by line segments contiguous (without lifting the pencil). If you join the consecutive points, you get a polygon regular of n sides (that's not funny). But if you join non-contiguous points (skipping from one, or two or three, etc.), are obtained polygons crashed sometimes and others Sometimes they are not crashed. Which are the Where are star-studded polygons? The 5-pointed star (so famous) is a example of them.
I came to the conclusion that if $n$ is odd we can build a star without lifting the pencil by jumping from a vertex, what more interesting things can be said? What happens if I jump from two vertices? I will form a star with what characteristics about $n$?