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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.

floran
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  • Do you have to give explicitly the isometry? – ajotatxe Jul 20 '15 at 12:10
  • Looks to me a nice problem in writing stuff out. Formulate an explicit isometry carrying one to the other, and show that generators for the two symmetry groups are conjugate. – John Brevik Jul 20 '15 at 12:57

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