REGULAR STAR POLYGONS

A star polygon is a star-shaped polygon that is formed by joining together the non-consecutive vertices in a regular polygon. 

To construct a star polygon inscribed in a circumference, we need to follow the same steps to draw a regular polygon, it depends on how many points of a star we want to draw.

So we must start finding the star points as they were the polygon vertices. Then we can join the non-consecutive points skipping one vertex, two or three vertices if the polygon has enough vertices to construct it. 

For example, the heptagon has two possible star polygons, skipping one vertex or two vertices.

Seven Pointed stars

             {7/2}                                              {7/3}

Here you can find the regular polygons and the star polygons that we can draw: