Regular star polygons

There are 3 possible cases.[br]1. [math]Step[/math] is divisor of [math]N[/math].[br]Then star is obtained by combining [math]Step[/math] copies of regular [math]N/Step[/math] - gons.[br]2. [math]Step[/math] is not divisor of [math]N[/math].[br] a). [math]N[/math] and [math]Step[/math] are co-prime. [br] Then we can see fully connected star with [math]N[/math] vertices.[br] b). [math]N[/math] and [math]Step[/math] have common factor other than 1.[br] Then we have degenerate small star with [math]N/GCD(N, Step)[/math] vertices.
Regular star polygons

Information: Regular star polygons