Compass and Straightedge Construction for Regular Heptagon does not exist/Proof 1

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There exists no compass and straightedge construction for the regular heptagon.


By definition, the regular heptagon has $7$ sides.

$7$ is a prime number which is not a fermat prime.

The result follows Construction of Regular Prime $p$-Gon Exists iff $p$ is Fermat Prime.