[Math] 2D figure with a nontrivial rotational symmetry

symmetry

I am stuck with following problem, could anyone help me?

(1) Can a finite 2D figure with a nontrivial rotational symmetry can have exactly one reflection symmetry?

thanks

Best Answer

Let $R_1$ be a nontrivial rotation that preserves the figure. Let $\phi_1$ be a reflection that preserves the figure.

What is $(\phi_1 R_1)^{-1}$?

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