We report intrinsic surface magnetism in pristine α rhombohedral boron (α-boron) using first-principles calculations. Semiconducting α-boron has been cleaved along the (001), (102̅), and (101) planes to produce icosahedral-based non-van der Waals face-boron, t-face-boron, and edge-boron structures, respectively. Face-boron is found to be metallic, while t-face-boron and edge-boron show semiconducting features. In particular, edge-boron exhibits layer-dependent magnetism with a transition from an overall antiferromagnetic (AFM) state with AFM surfaces to either an AFM or a ferromagnetic (FM) state with FM surfaces as the number of layers increases. The magnetism in edge-boron arises from the spin polarization of boron atoms with unsaturated bonds at the edge sites in the upper and lower surfaces, and magnetic exchange coupling can be mediated via adjacent boron icosahedra by up to a maximum of 8.4 Å. These findings deepen our understanding of icosahedral-based boron and boron-rich materials, which may be useful in potential spintronics applications.