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The High Efficiency Hybrid Cycle (HEHC) is a thermodynamic cycle which borrows elements of Diesel, Otto and Atkinson cycles, including: Air compression to a high ratio, followed by fuel injection and compression ignition (Diesel). Constant volume combustion (Otto) Over-expansion (Atkinson) Optionally, internal cooling heat recovery via steam generation (Rankine). Simple air standard analysis predicts this cycle to be 17% more efficient than diesel and 19% more efficient than Otto. The construction of a prototype rotary engine implementing this cycle is also described in detail. The main engine components consist of a rotor in pure rotation and two reciprocating gates directly driven by overhead cams. This combination separates the working mixture into three separate volumes. At a given rotor position each volume operates at a different part of the cycle. For instance, intake/compression, combustion, expansion/exhaust are occurring simultaneously in separate chambers.