The spatial scales of relativistic radio jets, probed by relativistic magneto-hydrodynamic (RMHD) jet launching simulations and by most very long baseline interferometry (VLBI) observations differ by an order of magnitude. Bridging the gap between these RMHD simulations and VLBI observations requires selecting nearby active galactic nuclei (AGN), the parsec-scale region of which can be resolved. The radio source 3C 84 is a nearby bright AGN fulfilling the necessary requirements: it is launching a powerful, relativistic jet powered by a central supermassive black hole, while also being very bright. Using 22 GHz globe-spanning VLBI measurements of 3C 84 we studied its sub-parsec region in both total intensity and linear polarisation to explore the properties of this jet, with a linear resolution of ∼0.1 parsec. We tested different simulation set-ups by altering the bulk Lorentz factor Γ of the jet, as well as the magnetic field configuration (toroidal, poloidal, helical). We confirm the persistence of a limb brightened structure, which reaches deep into the sub-parsec region. The corresponding electric vector position angles (EVPAs) follow the bulk jet flow inside but tend to be orthogonal to it near the edges. Our state-of-the-art RMHD simulations show that this geometry is consistent with a spine-sheath model, associated with a mildly relativistic flow and a toroidal magnetic field configuration.