Comment by libraryofbabel

A surprising related fact is that 200 years after Gauss and with a vast amount of progress in mathematics, we still don’t know the largest regular polygon with an odd number of sides that can theoretically be constructed in the Euclidean manner. For the curious, this is because the answer reduces to combinations of multiples of Fermat Primes, and nobody knows if there are any Fermat Primes beyond 3, 5, 17, 257, 65537. (See https://en.m.wikipedia.org/wiki/Constructible_polygon)