  We determine numerically the ground state of the two-dimensional, fully
polarized electron gas within the Hartree-Fock approximation without imposing
any particular symmetries on the solutions. At low electronic densities, the
Wigner crystal solution is stable, but for higher densities ($r_s$ less than
$\sim 2.7$) we obtain a ground state of different symmetry: the charge density
forms a triangular lattice with about 11% more sites than electrons. We prove
analytically that this conducting state with broken translational symmetry has
lower energy than the uniform Fermi gas state in the high density region giving
rise to a metal to insulator transition.
