Resch tessellations as stiff, folded modular shells

We present a method for designing and assembling modular, folded lattices based on numerically calculated triangular Ron Resch molecules. These lattices form stiff structural grids of beams capable of realizing both single- and double-curvature surfaces. Our work builds upon Ron Resch’s contributions to topology and geometry, where he first introduced folded tessellations as structural systems. His work laid the foundation for major advancements in architecture, structural engineering, and computational design, establishing him as a key figure in the emergence of Structural Origami as a distinct field. While much research has focused on the kinematic aspects of Resch’s work, we find a gap in its less explored potential for static structural applications. First, we describe how to compute triangular Ron Resch tripods to form a stiff and constrained unit cell, which we then assemble into a lattice. The resulting structure forms a woven hexagonal grid of beams with continuous second moment of inertia across the assembly, contributing to high stiffness. Next, we demonstrate how to numerically calculate developable unit cells to approximate target surfaces with single or double curvature. We believe this method—where global geometry and mechanical performance are encoded within the local crease pattern—offers significant potential for scalable structural folded shells, with applications from engineering to architecture.