A regular star polygon is an equiangular, equilateral, self-intersecting polygon formed by joining a vertex of a regular polygon with

*n*sides to another nonadjacent vertex and repeating this process until the first vertex is reached.To construct a star polygon with *p* vertices, we start by subdividing a circle into *p* equally spaced points forming congruent arcs. Then, starting from an initial vertex, we join that vertex to another vertex located *q* positions from it, so that *p* and *q* are relatively prime numbers and the points thus connected are separated by at least one point.

For example, for a regular star pentagon (5), which is a five-pointed star, the first point is connected to the third point (+2), then the third to the fifth (+2), then the fifth to the second (+2), then the second to the fourth (+2) and last, the fourth to the first (+2).

### Examples

- This is the regular star polygon (5 sides with 2 skips).

The numbers 5 and 2 are relatively prime.

- This is the regular star decagon (10 sides with 3 skips)

The numbers 10 and 3 are relatively prime.Note that the regular star decagon 10_{3}and the regular star polygon 10_{7}are equal.