A self-forming socket having a plurality of retractable pins bundled in parallel within a housing is disclosed. The bundled pins may displace longitudinally and are biased by spring force away from a frame onto which the pins are slidably held. A spacer pin may be positioned at the center of the socket and is similarly biased away from the frame under spring force. When the socket is forced over a fastener, nut, or bolt head, groups of pins are pushed inward toward the frame and into the housing thereby conforming the pins to the contours of the fastener. Applying a torque to the socket transfers the torque through the bundled pins to the fastener. Each pin has a circular cross-section and the interior walls of the housing containing the bundled pins has a hexagonal shape and does not contain any right angles. The pins are packed in a hexagonal arrangement.