An internal combustion engine operates on a six-stroke combustion cycle including a first compression stroke, a first power stroke, a second compression stroke, and a second power stroke. A first fuel charge is introduced to a combustion chamber of the engine at a first fuel rate during the first compression and/or first power stroke to produce lean exhaust gasses. A second fuel charge is also introduced to the combustion chamber during the second compression and/or second power stroke to normally produce lean exhaust gasses. Periodically, the second fuel charge can be increased to a second fuel rate to produce stoichiometric rich exhaust gasses. A lean nitrogen oxide trap can be disposed in an exhaust system associated with the engine to temporarily trap nitrogen oxides. Once saturated, the LNT can be periodically regenerated by production of the rich exhaust gasses.