The self-assembly of rigid three-legged building blocks into polyhedral cages is investigated by patchy particle simulations. A four-site anisotropic interaction potential is introduced to make pairs of overlapping legs bind in an anti-parallel fashion, thereby forming the edges of a polyhedron of pentagons and hexagons. A torsional potential, reflecting an asymmetry or polarity in the legs' binding potential, proves crucial for the successful formation of closed fullerene-like cages. Self-assembly proceeds by a nucleation-and-growth mechanism, with a high success rate of cage closure. The size distribution of the self-assembled buckyballs is largely determined by the pucker angle of the particle. Nature explores a similar building block, the clathrin triskelion, to regulate vesicle formation at the cell membrane during endocytosis.