Multistep Evolution Method to Generate Topological Interlocking Assemblies

Research on topological interlocking (TI) assemblies indicates that the geometry of blocks plays a significant role in the performance of a configuration. The current TI generation methods can return assemblies of uniform antiprisms, tetrahedra, cubes, and octahedra. However, other shapes (both convex and concave) are well qualified for use in TI assemblies. This paper presents a framework to generate blocks for TI assembly. Starting from a seed polygon, evolution steps translate and reshape the polygon, contracting it eventually to a point, a line segment, or another polygon. Our framework generalizes and unifies previous-generation methods based on tilting angles and height parameters. We show how the proposed method systematically generates novel TI solids and previously reported others.