A polygonal coupling couples torque source to a torque consumer such that input and output portions of the coupling may elastically rotate relative to one another during torque transfer to accommodate rotational speed variations in delivery of torque from the torque source. In an embodiment the torque source is an internal combustion engine with an integrated switchable coupling between the engine crankshaft and a torque transfer segment supporting a motor-generator. The polygonal coupling includes axially-overlapping polygonal-shaped male and female portions which cooperate to pass torque between the output of the integrated switchable coupling and an input of the torque transfer segment. At least one of the male and female portions includes recesses which form flexible arms adjacent to the lobes of the polygonal shape that allow the portions to rotate relative to one another over small angular displacements, and thereby improve damping of crankshaft rotational vibrations.