Compass and Straightedge Construction for Regular Heptagon does not exist

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

Proof
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.