Crystal morphologies are important for the design and functionality of devices based on low-dimensional nanomaterials. The equilibrium crystal shape (ECS) is a key quantity in this context. It is determined by surface energies, which are hard to access experimentally but can generally be well predicted by first-principles methods. Unfortunately, this is not necessarily so for polar and semipolar surfaces of wurtzite crystals. By extending the concept of Wulff construction, we demonstrate that ECSs can nevertheless be obtained for this class of materials. For the example of GaN, we identify different crystal shapes depending on the chemical potential, shedding light on experimentally observed GaN nanostructures. 68.35.Md,68.47.Fg,81.10.Aj Low-dimensional semiconductor nanostructures have attracted a lot of interest in the past decades, largely due to their applications in low-energy consumption and energyharvesting devices [1,2]. Owing to surface effects, the performance of such devices strongly depends on the nanocrystal morphology. To achieve comprehensive understanding and control of the preferred growth morphology, one must know the material's natural shape that results from its crystallographic anisotropy. Ab initio theory can generally provide more insight into this complicated issue through the calculation of surface energies since, according to Wulff's theorem [3], the equilibrium crystal shape (ECS) of a solid can be constructed by the mere knowledge of surface energies of various crystal planes. For a crystalline solid, the surface energy γ is defined as the excess free energy required to create one unit of surface area A [4],G represents the Gibbs free energy of the system that, neglecting temperature and pressure, is replaced by the total energy. The chemical potential µ i is the free energy per atom in the system for species i, and N i denotes the number of atoms of this species. In a bulk material, the total chemical potential is known from the corresponding total energy E bulk = ∑ i n i µ i , where n i is the number of atoms of species i in the bulk. Hence, the surface energy of a nonpolar plane can be extracted from density-functional-theory (DFT) results for a slab that contains two identical surfaces well separated from each other. For some polar and semipolar planes, however, individual surface energies are difficult to access, because different facets may appear at the two surfaces of the slab. To overcome this problem, a method has been proposed [5] involving two surface types on three side faces of a triangular wedge. This approach is, however, not applicable to all surfaces and crystal structures; polar surfaces in wurtzite crystals are one example [6,7]. Consequently, not every individual surface energy of wurtzite crystals can be computed; hence, the construction of the ECS seemed impossible. Recently, neglecting the different layer-stacking sequence, the surface energy of the polar c plane was estimated from the zincblende (111) plane [10].In this Letter, we show that such an approxim...