Theorem 3.5: There are 2n(k - 1) + n edges in a {n/k} star.

proof 1: We can use the famous result of Euler's that if p = the number of points in the figure, e = the number of edges, and a = the number of faces that

p - e + a = 1

From this we can solve

e = p + a - 1

and substituting from the last two results we get

e = (nk) + (1 + nk - n) - 1

which simplifies to

e = 2n(k - 1) + n

proof 2: There are n sides to the central n-gon. At the other n(k - 1) points, there are two edges that meet at that point.

Return to text