The structure and energetics of an isolated {111} stacking fault and the interactions of two non-coplanar {111} stacking faults in zincblende GaN are investigated using an empirical potential of the Tersoff-Brenner type. For a single stacking fault, a metastable configuration is found only when the fault is created on the {111} plane in the glide set, which results in local transformation into a more stable wurtzite structure. This energetically favorable configuration is separated from the unfaulted crystal by a large energy barrier. Interactions between two stacking faults on non-coplanar {111} planes, where one fault corresponds to the metastable configuration created in the glide set and the second fault is created on a different {111} plane, lead to a reduction of the aforementioned energy barrier and an increase of the energy of the second metastable fault. The intersection of the two faults results in a significant reconstruction of atomic positions around the line common to both faults. Apart from the wurtzite stacking, the structure of this intersection shows a partial transformation into the rocksalt structure that is normally stable only at high pressures. The presence of this high-energy rocksalt structure is avoided if the second fault is non-planar. In this case, four different structures of the intersection exist. We demonstrate that one of these structures agrees well with TEM observations.