A reconfigurable hardware-geometry system for the assembly of multiple structures from finite panel kits and adaptable nodes

This paper presents an integrated hardware-geometry framework for approximating semi-freeform shell and spatial structures through a finite kit of rigid panels and a reconfigurable 3D-printed vertex joint. Connecting exactly three panels at a shared vertex, the joint combines a continuous dihedral fold range of −50° (closing) to +10° (hyperextension) about flat with ±30° of in-plane rotation around a neutral 120° configuration, and its geometry requires the projected arm directions to sum to 360° in the connection plane, accommodating convex panel corners of 90–150° . These bounds define a constrained design space in which doubly curved geometries can be approximated without bespoke components. A complementary digital workflow rationalises freeform surfaces into this space: candidate panels harvested from planarised hex-dominant meshes are clustered into a finite kit of convex polygonal types by data-driven analysis of edge lengths and internal angles; valid three-panel vertex configurations (triads) are enumerated with every dihedral constrained to the joint’s fold range; and an integer linear programme selects a non-overlapping subset from a redundant pool of surface-anchored candidate placements, maximising panel-to-panel edge bonding whilst steering the curvature-correct tile to each location. The method thereby turns a design intent into an enumerated family of buildable discrete structures assembled from one finite kit of parts.