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The magnetocrystalline anisotropy energy of atomically ordered L10 FeNi (the meteoritic mineral tetrataenite) is studied within a first-principles electronic structure framework. Two compositions are examined: equiatomic Fe0.5Ni0.5 and an Fe-rich composition, Fe0.56Ni0.44. It is confirmed that, for the single crystals modeled in this work, the leading-order anisotropy coefficient K1 dominates the higher-order coefficients K2 and K3. To enable comparison with experiment, the effects of both imperfect atomic long-range order and finite temperature are included. While our computational results initially appear to undershoot the measured experimental values for this system, careful scrutiny of the original analysis due to Néel et al. [J. Appl. Phys. 35, 873 (1964)] suggests that our computed value of K1 is, in fact, consistent with experimental values, and that the noted discrepancy has its origins in the nanoscale polycrystalline, multivariant nature of experimental samples, that yields much larger values of K2 and K3 than expected a priori. These results provide fresh insight into the existing discrepancies in the literature regarding the value of tetrataenite’s uniaxial magnetocrystalline anisotropy in both natural and synthetic samples.