Using the two-dimensional Wulff plot, the equilibrium shape of a sapphire crystal was investigated as a function of surface energy anisotropy. Depending on the relative values of surface energy for various facet planes, the projected shape of equilibrium sapphire was determined to be rectangle, parallelogram, hexagon or octagon. The results are compared with the experimentally observed shapes of internal cavities of submicron range in sapphire single crystals.