Highly-versatile variable-angle bone plate system

A bone plate system for internal fixation of bone fractures includes a bone plate having a plurality of bone plate holes. The holes are constructed to receive either a non-locking, locking, or variable-angle locking bone screw. The holes have discrete columns of teeth or thread segments arranged around the inner surface of the hole for engaging threads on the heads of locking and variable-angle locking bone screws. Conventional locking bone screws engage the bone plate coaxially with the central axis of the bone plate hole. Variable-angle locking bone screws can engage the bone plate at a selectable angle within a range of selectable angles relative to the central axis of the bone plate hole. The head of the variable-angle locking screw is at least partially spherical, and the thread thereon has a profile that follows the arc-shaped radius of curvature of the spherical portion of the screwhead.