The number of unique n-point stars that can be drawn is related to phi
(n), the totient of n.  

The totient of n is the number of numbers that are "coprimes" of n. This 
means they have no common factors with n. The number 60 has the 
following coprimes:

1 7 11 13 17 19 23 29 31 37 41 43 47 49 53 59

It can be shown that

phi(n) = n * (p1-1)/p1 * (p2-1)/p2 ...

where the p's range over the unique prime factors of n.

The number of n-point stars = (phi(n)-2)/2 

Since 60 = 2 * 2 * 3 * 5, we have

phi(60) = 60 * 1/2 * 2/3 * 4/5 = 16

The number of unique 60-point stars = (16-2)/2 = 7