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.

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