Abstract: A furniture interconnection system for reversibly joining a board element and an upright element perpendicular to each other in a furniture frame. The joint is formed by a tenon and a mortise, the tenon having a novel irregular hexagon shape, the mortise having a novel irregular quadrilateral shape. The tenon is inserted into the mortise and pivoted in stages on a pair of angles of the hexagon, to form a stable joint without fasteners such as glue, screws, and other similar fasteners. As the tenon pivots inside the mortise, pairs of complementary and supplementary angles interact within the furniture interconnection system to position the tenon to form the stable joint without additional fasteners, allowing the furniture frame to be easily dismantled for moving or reconfiguration without damaging the frame, but forming the reversible joint that is sufficiently sturdy to support the load it was designed to bear.