The wankel engine uses a curved triangle within an almost "8-shaped" chamber to create chambers of compression. The internal shaft (A, see animation on the right) rotates three times to every one cycle of the rotor (B, refer to animation).
These engines do not require valves, because the intake and exhaust chambers are always open. Although they are mechanically simple, these engines are rarely mass-produced due to reliability issues that can result from poor geometrical engineering. Currently, the only auto manufacturer to mass-produce this engine is Mazda, in models such as the RX-7 and RX-8. The engine has found its way into other applications, often due to its impressive power-to-weight ratio.
Images courtesy of Wikimedia Commons.