A torque enhancement device having one or more torque enhancement member(s) with each having an exterior (preferably bi-symmetric or essentially bi-symmetric) surface configuration with parallel, longer side walls extending in a Y-axis direction and shorter side walls extending in an X-axis direction and corner recesses positioned between ends of adjacent longer and shorter side walls, and with some embodiments of the invention featuring a torque enhancement device having a hole extending in a Z-axis direction. A fastener assembly is also provided that includes one or more torque enhancement devices as well as methods for utilization of the torque enhancement device or utilization or assemblage of an assembly including a torque enhancement device. The surface configuration includes arrangements where there is a torque differential in one direction or the other as well as arrangements that are adapted to handle both standard fastener configurations and torque enhancement configurations with a common torque enhancement device.
