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Let $\Omega$ be a bounded annular $C^{1,1}$ domain in $\mathbb{R}^2$ which isleft invariant under the action of the dihedral group $D_n$ of isometries of$\mathbb{R}^2$ .We show that the nodal line of a second Dirichlet eigenfunctionmust intersect the boundary of $\Omega$, under suitable conditions on$\frac{\partial}{\partial \theta}$ .

On the nodal line of a second eigenfunction of the Laplacian-Dirichlet in some annular domains with dihedral symmetry