The {15/7} star is an interesting example.

Inside {15/7} we find the {15/6} star

which consists of three five pointed stars. Inside of {15/6} we find a {15/5} star. Since the stars are getting more and more delicate as we get closer to the center, we will enlarge the inner stars to make them easier to see.

The {15/5} star consists of 5 equilateral triangles. Inside {15/5} we find a {15/4} star

which is a simple star. Inside that is {15/3}

which consists of three regular convex pentagons. Inside that is {15/2}

which is another simple star, and inside that is {15/1} which is a regular convex 15-gon.