Geometrically Interlocking Space-Filling Tiling Based on Fabric Weaves

In this article, we introduce a framework for the geometric design and fabrication of a family of geometrically interlocking space-filling shapes, which we call woven tiles. Our framework is based on a unique combination of (1) Voronoi partitioning of space using curve segments as the Voronoi sites and (2) the design of these curve segments based on weave patterns closed under symmetry operations. The underlying weave geometry provides an interlocking property to the tiles and the closure property under symmetry operations ensure single tile can fill space. In order to demonstrate this general framework, we focus on specific symmetry operations induced by fabric weaving patterns. We specifically showcase the design and fabrication of woven tiles on flat and curved domains by using the most common 2-fold fabrics, namely, plain, twill, and satin weaves. We further evaluate and compare the mechanical behavior of the so created woven tiles through finite element analysis.