The electronic band structure of a newly characterized polysilane (Si6H6) Sheet has been studied with Hartree-Fock and local density-functional calculations. A direct band gap was found with a calculated absorption edge at 3 eV. Layered structures (Si6nH6) With thicker Si sheet cores can be constructed by linking several layers followed by hydrogen termination of the exposed surfaces. The multiply linked materials are found to develop a weak indirect band gap approaching that of bulk silicon as the number of layers increases. The observed band-gap variation in hydrogen-passivated porous silicon (p-Si) may be related by recognizing that the p-Si is made of cross-linking Si sheet structures (Si6nH6) whose Si core thickness (n) varies with preparation conditions.