Theorem 3.2: (Coxeter [4] ) If 1 < k < n/2, then for all 1 < j < k there will be an {n/j} star inside {n/k}.

proof: By reverse induction on j. Inside the {n/k} star is an {n/k-1} star by Theorem 3.1. Inside the {n/k-1} star there is an {n/k-2} star also by Theorem 3.1. Continue until we get that inside the {n/2} star there is a {n/1} star. This last star is of course a regular n-gon.

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