We studied the energetics and electronic structure of polymerized benzene hollow-cages and sheet using the density functional theory with the generalized gradient approximation. The energetics and electronic structure of the polymeric benzene cages and sheet depend on their size and dimensionality. Because of the symmetric network topology as well as the constituent benzene units, the cages possess highly bunched states around the Fermi level. The energy gap between the highest occupied and the lowest unoccupied states of the cages is approximately proportional to their curvature, owing to the decrease of the strain. The polymerized benzene sheet is a direct gap semiconductor with the gap of 2.4 eV between the less dispersive states of the highest branch of the valence and the lowest branch of the conduction bands.