Sockets, for example, hexagon sockets, dodecagonal sockets, and splined sockets, that have inner surface geometries adapted to engage a flank of a fastener at a point away from a corner of the fastener. In general, the sockets engage the flank of the fastener at a distance of about 30 to 60 percent of half a length of the flank away from the corner of the fastener. This increases the strength and life of the socket, reduces a risk of the fastener becoming locked or stuck in the socket, and reduces the risk of the fastener being stripped or the socket slipping on the fastener.