A rotary kiln having a polygonal lining is disclosed for pyro-processing cement, lime, other minerals, as well as other materials. Specifically, utilizing a polygonal lining of brick or a refractory or ceramic material having between 3 and 12 sides improves the heat efficiency or heat transfer between high-temperature gases and a burden of material to be processed by the kiln. Such an efficient utilization of the gas heat is due to various factors which cause a larger amount of the burden to be more quickly exposed to the high temperature gases. These various factors include increased tumbling, increased residence time, decreased degree of filling, and increased surface exposure.