Different magnetic anisotropies and magnetization reversal mechanisms were identified in magnetic nano-objects of four-fold symmetry, using micromagnetic simulations. Nano-particles with lateral dimensions between 50 nm and 400 nm, simulated with typical properties of permalloy, iron and cobalt, were tested in dependence of the angular orientation with respect to the externally applied magnetic field. All nano-objects exhibited steps on the sides of the hysteresis loops, which can be correlated with stable intermediate states at remanence, for some angular regions. Coercive fields were found to show an irregular and unpredictable angular dependence in case of cobalt nano-particles, while this material depicted the largest number of steps in general. Comparing the angular dependence of the coercive fields with previous calculations, it was shown that usual descriptions of fourfold anisotropies are no longer valid in most of the nano-objects under examination.