The present work is a systematic study of tetrataenite's magnetic behavior based on micromagnetic simulations. Tetrataenite, a Fe50Ni50 intermetallic compound with L10 structure, is a chemically ordered alloy normally found in meteorites. In natural samples, like in meteorites, tetrataenite occurs as islands or clusters embedded in other Fe-Ni alloys. Its composition as well as its high magnetic anisotropy and magnetization make it a material of great technological application potential. Several properties of interest were studied in the simulations, such as the exchange coupling, magnetic texture, and particle size. The intention is to describe the tetrataenite's general magnetic behavior in order to assist the interpretation of experimental results and predict different scenarios which may occur in natural meteoritic samples. The results show the effects of the exchange magnetic coupling play an important role in the reversal of the magnetization, but they are less determinant for the coercivity than the effects of texture and island size. It is also concluded that the initial state is more decisive for the determination of the equilibrium state than the magnitude of the magnetic coupling between the islands and matrix.