**Theorem 2.2**: (Coxeter
[4]) {n/k} is a simple star if and
only if n and k are relatively prime.

**proof**: Label the points of the star with the elements of
Z_{n}. When you proceed from one point to the next, following
the star, to get to the next point, you add (or subtract, depending
on whether you are proceeding clockwise or counterclockwise) k to the
index of each point using arithmetic modulo n. As a result, if you
start at the 0 point, you will trace out the cyclic subgroup in
Z_{n} generated by k. It is well known
[7] that this subgroup fills up
all of Z_{n} if and only if k is relatively prime to n.