Transmitting torque from a housing to a drive shaft by configuring contact surfaces between a housing and shaft to increase the transmission of torque. Tools such as drilling tools often require torque to be transmitted from a rotating housing to a driveshaft. This is often accomplished through threaded connections or splines. A threaded connection can be used to transmit torque by allowing two pieces to be securely joined by rotating and tightening to a specified torque. A splined connection can also be used to transmit torque, providing sufficient clearance for one member to slidingly receive the other without rotating and torqueing. A tapered polygon may be used to transmit torque that by virtue of tapering can take up clearances between the torque carrying components. As such, the tapered polygon does not introduce significant stress concentrations into the components.