Multi-tier torque enhancer driver and/or receiver and method of using same

A multi-tier torque enhancing device, comprising:

• a torque contact device having radially or axially, or both radially and axially, separated torque contact surface configurations, wherein
• at least one of the one or more torque contact surface configurations provides an enhanced torque contact surface configuration comprising a pair of X-axis extending torque contact side walls, of an X-axis extension length, that are spaced apart by L1 along a Y-axis, and a pair of Y-axis extending torque contact side walls, of a Y-axis extension length, that are spaced apart by L2 along an X-axis, as well as four concave contoured surface portions positioned between respective adjacent ends of the X-axis extending torque contact side walls and the Y-axis extending torque contact side walls, and the enhanced torque contact surface having an L2/L1 ratio that is less than 1, and wherein the enhanced torque contact surface configuration is configured to be operated by a torque generation tool or is configured to operate as a torque generation tool,
• wherein, relative to an X-Y axes plane that extends through each of the X-axis and Y-axis extending torque contact walls and at a Z-axis location where the X-axis extending torque contact side walls are radially most removed from the Z-axis, a maximum radial extension amongst the four concave contoured surface portions on that X-Y axes plane, that is defined by a radial extension from a circumference falling on end points of one of the Y-axis extending walls to a point on an adjacent-most concave contoured surface portion closest to the Z-axis, is less than at least one of said Y-axis and X-axis extension lengths on that X-Y axes plane,
• wherein the concave contoured surface portions span and directly interconnect the respective adjacent ends of the X-axis and Y-axis extending side walls between which the respective concave contoured surface portions extend,
• wherein said Y-axis extension length is longer than said X-axis extension length, and
• wherein all, or at least a majority, of each Y-axis extending torque contact side wall extends along a straight, or substantially straight, line, and said line extends perpendicular or substantially perpendicular to L2 when L2 intersects with the Z-axis.