Fullerene C60 monomer crystals were compressed to a face-centered cubic (fcc) phase with a lattice parameter of a = 11.93(5) Å and a micro-Vickers hardness of 4500 kg/mm2 using high-pressure and high-temperature conditions of 15 GPa at 500-600°C. The hardness is compatible with that of cubic boron nitride (c-BN), suggesting the formation of a 3D C60 polymer. The single-crystal X-ray structural analysis revealed that each C60 molecule in the polymer was linked to the 12 nearest neighbors by [2+2] cycloaddition between the common pentagon-hexagon (56) edges. However, ab initio geometry optimization and molecular dynamics calculations suggested that the 3D polymer should have a rhombohedral structure with the space group of R3 containing [3+3] cycloaddition between the pentagons of C60 molecules within the plane perpendicular to the 3-fold axis. The higher apparent symmetry of fcc was observed as an averaged structure of different orientations of the rhombohedral structure. The R3 structure can be derived by only a slight rotation of each C60 unit in the (111) plane of the fee structure. The band-structure calculation suggested that the 3D polymer (R3) was a semiconductor; the activation energy for the electrical conductivity was experimentally determined to be 0.25 eV at 550 K.