Micromagnetic calculations have been carried out for spherical magnetite particles with surface roughness consisting of patterns of conical bumps based on regular (Platonic) convex polyhedra. The purpose was to examine the effect of surface irregularities while avoiding overall shape anisotropy, which generally plays a dominant role in determining hysteresis properties. We considered three morphologies based on the tetrahedron (4 apices), the icosahedron (12 apices), and the dodecahedron (20 apices). Grains of three sizes were considered: 30 nm (single-domain, SD), 90 nm (on the single-domain/pseudo-single-domain boundary, SD/PSD), and 120 nm (stable pseudo-single-domain, PSD). We find that the morphologies investigated have very little effect on the hysteresis parameters of SD and marginal SD/PSD grains. However, in the PSD grains, coercivity increases significantly as bump amplitude increases from 0.1 to 0.9. This lends support to the long-standing notion that surface protuberances on larger grains are a possible source of paleomagnetically significant stable remanence, although the very high coercivities (on the order of 100 mT) observed in some rocks cannot be achieved. Classical Stoner-Wohlfarth shape anisotropy remains the only explanation for such ultra-stable remanence in magnetite-bearing rocks. This is confirmed by a specific example of a model “skeletal” grain consisting of three orthogonal parallelepipeds.