In this paper we discuss a rotary implementation of the High Efficiency Hybrid Cycle (HEHC) engine. HEHC is a thermodynamic cycle which borrows elements of Diesel, Otto and Atkinson cycles, characterized by 1) compression of air only (e.g. Diesel), 2) constant volume heat addition (e.g. Otto), and 3) expansion to atmospheric pressure (e.g. Atkinson). The engine consists of a compressor, an isolated combustion chamber, and an expander. Both compressor and expander consist of a simple design with two main parts: a rotor and an oscillating rocker. Compared to conventional internal combustion engines, in which all processes happen within the same space but at different times, in this engine, all processes are occurring simultaneously but in different chambers, allowing for independent optimization of each process. The result is an engine which may offer up to 57% peak efficiency, and above 50% sustained efficiency across typical driving loads.