It is customary to evaluate the efficiency of four-stroke-cycle heat engines such as Carnot, Otto and Diesel with a working ideal gas [1] [2] [3]. Here we consider various three-stroke-cycle heat engines that are composed of three out of four special processes: adiabatic, isothermal, isobaric and isochoric. We deviate from the customary norm considering the working material to be a polyatomic ideal gas with various degrees of freedom. We develop analytic expressions for the efficiency of each design as a function of degrees of freedom. For suitable practical values of relevant (V, P, T), we evaluate the corresponding efficiencies.