A number of periodic lattices have historically been used to represent ice-lh in computer simulations. These vary in size, shape, and method of generation, and while they have served their intended purposes, their properties have rarely been documented in detail and their intercompatibility is unknown. We develop a method for generating sets of internally consistent lattices and apply it to determine eight unit cells containing from 96 to 768 water molecules in both near-cubic and slab arrangements. It can easily be applied to generate additional (larger) cells or representations of specific crystal faces. Each unit cell in this set has zero net dipole moment and minimal net quadrupole moment and is optimized using four different criteria to measure the randomness of the hydrogen bonding; if required, these criteria can easily be modified to suit the intended application and alternate sets thus generated. We find that Cota and Hoover’s much used constraint for selecting unit cells with zero dipole moment is too restrictive, not permitting a fully random hydrogen-bonding network; also, unit-cell generation methods based on potential-energy minimization are found to prefer unrepresentative, highly ordered structures.