The ground state of a three-dimensional electron gas is theoretically investigated within the framework of the local spin density approximation with the Perdew-Zunger exchange-correlation energy. The system has been found to be in a one- or two-dimensional crystal state, when the Wigner sphere radius r(s) has an intermediate value. At r(s) = 60, a triangular lattice with the lattice spacing 96.10 is the lowest energy state among fluids, 1D, 2D, and 3D crystals.