Let $P_1$ and $P_2$ be regular n-gons in $E^2$ with centers $C_1$ and $C_2$. Prove that $Sym(P_1)$ and $Sym(P_2)$ are conjugate in $Isom(E^2)$.
Hi,
I have to prove this but it looks very obvious to me. But I don't know how to write it and where can I use the centers? It looks like an unnecessary information.