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We present the first comparison of multiple global simulations of the solar wind interaction with Mercury's dayside magnetosphere, conducted in the framework of the international collaborative project SHOTS - Studies on Hermean magnetosphere Oriented Theories and Simulations. Two 3D magnetohydrodynamic and two 3D hybrid simulation codes are used to investigate the global response of the Hermean magnetosphere without its exosphere to a northward-oriented interplanetary magnetic field. We cross-compare the results of the four codes for a theoretical case and a MESSENGER orbit with similar upstream plasma conditions. The models agree on bowshock and magnetopause locations at 2.1 ​± ​0.11 and 1.4 ​± ​0.1 Mercury planetary radii, respectively. The latter locations may be influenced by subtle differences in the treatment of the plasma boundary at the planetary surface. The predicted magnetosheath thickness varies less between the codes. Finally, we also sample the plasma data along virtual trajectories of BepiColombo's Magnetospheric and Planetary Orbiter. Our ability to accurately predict the structure of the Hermean magnetosphere aids the analysis of the onboard plasma measurements of past and future magnetospheric missions.