the Gauss-Wantzel theorem:
:A regular n-gon is constructible with straightedge and compass if and only if n = 2^kp₁p₂...p_t where k and t are non-negative integers, and the p_i's (when t > 0) are distinct Fermat primes.

The five known Fermat primes are:
:F₀ = 3, F₁ = 5, F₂ = 17, F₃ = 257, and F₄ = 65537 .

Since there are 31 nonempty subsets

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