Low-energy electron diffraction patterns, produced from quasicrystal surfaces by ion sputtering and annealing to temperatures below ∼700 K, can be assigned to various terminations of the cubic CsCl structure. The assignments are based upon ratios of spot spacings, estimates of surface lattice constants, bulk phase diagrams vs surface compositions, and comparisons with previous work. The CsCl overlayers are deeper than about five atomic layers, because they obscure the diffraction spots from the underlying quasicrystalline substrate. These patterns transform irreversibly to quasicrystalline(like) patterns upon annealing to higher temperatures, indicating that the cubic overlayers are metastable. Based upon the data for three chemically identical, but symmetrically inequivalent surfaces, a model is developed for the relation between the cubic overlayers and the quasicrystalline substrate. The model is based upon the related symmetries of cubic close-packed and icosahedral-packed materials. The model explains not only the symmetries of the cubic surface terminations, but also the number and orientation of domains.