**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.