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 103 and the regular star polygon 107 are equal.
