ABSTRACTWe report the electronic structure of the S46 lattice having a just lnm-size unit cell and has been optimized within the density-functional theory. The Si46 lattice studied is the real geometry of Si atoms crystallized with metal atoms, and consists essentially of dodecahedral-cage Si20 fullerenes proposed by us previously. Although all the Si atoms are tetrahedrally coordinated, its electronic structure is found to be considerably different from that of the diamond Si lattice due to the pentagonal Si-Si network. Si46 is an important new Si semiconductor to be synthesized in the future. We also report the electronic structure of Na2Ba6Si46. The material is found to be metallic and the Fermi-level density of states is very high due to the hybridization between Si and Ba states, which should be of essential importance for the superconductivity observed in Na and Ba codoped Si46.