**Theorem 3.1**: (Coxeter
[4]) If 1 < k < n/2, then
inside an {n/k} star is an {n/k-1} star.

**proof**: In a general {n/k} star, k > 1, consider the
points where the lines from adjacent points on the star meet. If n is
even and k = n/2, then all of the lines will meet at the center of
the circle, but, if 1 < k < n/2, then it follows from symmetry
considerations that this will produce n distinct points which will be
equally spaced on a circle. Since the number of spaces between a
number of points of a star is always one less than the number of
points, the lines in the outside star will connect each point in the
inside figure with the point k-1 points away. Thus they will form an
{n/k-1} star.