Internal combustion engines that use the pumping motion of the engine pistons to supercharge the cylinder with air/charge are disclosed. The pistons may include a skirt with a field of pockets that provide a ringless, non-lubricated, seal equivalent. The piston heads may be domed with one or more depressions to facilitate the movement of air/charge in the cylinder. The engines also may have non-circular, preferably rectangular, cross-section pistons and cylinders. The engines also may use multi-stage poppet valves in lieu of conventional poppet valves, and may include a split crankshaft. The engines also may operate in an inverted orientation in which the piston is closer to the local gravitationally dominant terrestrial body's center of gravity at top dead center position than at bottom dead center position.