  We consider a Fr\"ohlich polaron bound in a symmetric Mexican hat-type
potential. The ground state is unique and therefore invariant under rotations.
However, we show that the minimizers of the corresponding Pekar problem are
nonradial. Assuming these nonradial minimizers are unique up to rotation, we
prove in the strong-coupling limit that the ground-state electron density
converges in a weak sense to a rotational average of the densities of the
minimizers.
