Internal combustion engines that 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 are disclosed. The engines may have non-circular, preferably rectangular, cross-section pistons and cylinders, and the pistons may include a skirt with a field of pockets that provide a ringless, non-lubricated, seal equivalent. The pistons also may have a domed piston head with depressions thereon to facilitate the movement of air/charge in the cylinder. The engines also may use multi-stage poppet valves in lieu of conventional poppet valves, and a split crankshaft. The engines may use the pumping motion of the engine piston to supercharge the cylinder with air/charge.