  We determine 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 $\sim 3$)
we obtain a ground state of different symmetry: the charge density forms a
triangular lattice with about 11% more sites than electrons. We argue that this
conducting state with broken translational symmetry remains the ground state of
the high density region in the thermodynamic limit giving rise to a metal to
insulator transition.
