||The buckling of hexagonal layers in bulk and nanostructures of AlN is analyzed in the framework of atomistic and first principles techniques. At ambient conditions, the wurtzite structure (B4) of AlN consists of buckled hexagons. On the other hand, a non-buckled B$_k$ structure is found to be metastable at zero pressure, being favored at higher pressures. It is suggested that the energy ordering of B4 and B$_k$ may change in finite systems; an assertion tested in this study by considering finite slabs, nanobelts, and nanorings, and comparing the results with the previous studies on small clusters, and periodic nanostructures. We find that the buckling in finite systems is much smaller than that in the bulk material, with N atoms sticking out in the first layer, followed by an even smaller opposite buckling of the next layer, and negligible buckling of the inner layers. All the structures considered present some degree of symmetry, usually a$\sigma _z$ symmetry plane, so that buckling is opposite on both sides of the finite system and thus the dipole moment is quenched. Periodic nanostructures display no buckling, a fact that is related with their ability to model the inner part of the system, neglecting geometric surface effects. It is suggested that the zero-dipole and negligible buckling present in the small size regime will lead to buckled hexagons in larger finite systems, similar to the bulk behavior, thus introducing a change in the size dependence of their structural and electronic properties.