A regular n-gon can be constructed with compass and straightedge only if n is the product of a power of 2 and any number of distinct Fermat primes.
Fermat number = 2^2^n + 1
Known Fermat primes = 2,5,17,257,65537
Constructible = 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24
Not constructible = 7, 9, 11, 13, 14, 18, 19, 21, 22, 23, 25