A rotary combustion engine includes a peripheral housing, a front housing plate, a rear housing plate, a piston, and an eccentric shaft, where the piston rotates to form three working spaces separated from each other by the tips of the piston. Shaft seals and piston seals seal off the oil-carrying interior space of the internal combustion engine, and the piston is sealed off against the front and rear housing plates by arcuate strips, which are bounded radially on the inside by an envelope curve. The gas forming in the working space during the combustion phase is under high pressure. Some of this gas leaks around the arcuate strips and flows inward along the flat surfaces of the front and rear plates by way of ring-shaped channels in the piston, thus arriving in recessed areas inside the envelope curves, from which it is then escapes through vent channels.