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By this theorem, we can construct all of the first 10 regular polygons from an [[equilateral triangle]] up to a [[duodecagon]], with the exception of a [[heptagon]]. As 7 is not a Fermat prime nor has it any factors which are Fermat primes, a regular heptagon therefore cannot be constructed by straightedge and compass alone.

By this theorem, we can construct all of the first 8 regular polygons from an [[equilateral triangle]] up to a [[decagon]], with the exception of a [[heptagon]]. As 7 is not a Fermat prime nor has it any factors which are Fermat primes, a regular heptagon therefore cannot be constructed by straightedge and compass alone.