The disclosure relates to a lamp fitting apparatus system. A system includes a polygonal socket connector comprising a first tapered fitting, wherein the polygonal socket connector is configured to connect with a lamp socket. The system includes a polygonal bracket comprising a second tapered fitting, wherein the polygonal bracket is configured to attach to a lampshade. The system is such that the second tapered fitting of the polygonal bracket corresponds with the first tapered fitting of the polygonal socket connector, such that the polygonal bracket and the polygonal socket connector form a compressing fitting configured to connect the lampshade to the lamp socket.