  The ground state of a two-dimensional electron gas at Landau level filling
factors near $\nu =1$ is a Skyrme crystal with long range order in the
positions and orientations of the topologically and electrically charged
elementary excitations of the $\nu=1$ ferromagnetic ground state. The lowest
energy Skyrme crystal is a square lattice with opposing postures for
topological excitations on opposite sublattices. The filling factor dependence
of the electron spin-polarization, calculated for the square lattice Skyrme
crystal, is in excellent agreement with recent experiments.
