The structural properties of the ionic conductor LiID2O have been studied by neutron scattering. The cubic room temperature α-phase, Pm3m, is disordered both with respect to the occupation of the Li+-positions and to the orientations of the water molecules. A first order phase transition from the α-phase to a new orthorhombic β-phase, P21am or Pmam, has been found at - 54°C. The structural parameters of the β-phase have been determined by the Rietveld method based on powder diffraction data. The β-phase is found to have an antiferroelectric ordering of the water molecules and a spatial ordering of the Li+-sites. Evidence for short range order is found in the diffuse elastic scattering in the α-phase and the implications for the ionic conductivity are discussed.