The pedal-polygon equivalence conjecture for n-gons

Let $G(n)$ be the set of $n$-gons, and let $\perp$ denote the equivalence relation generated by the pedal-polygon construction.

Pedal-polygon equivalence conjecture. For integer $n\ge 5$, if $G(n)$ is the set of $n$-gons, then

$$|G(n)/{\perp}|=1.$$

The preceding theorem establishes the analogous statement for quadrilaterals, while the assertion for all integers $n\ge 5$ is presented as a conjecture and its resolution is not supplied here.