Voronoi Spaghetti & VoroNoodles: Topologically Interlocked, Space-Filling, Corrugated & Congruent Tiles

In this work, we introduce an approach to model topologically interlocked corrugated bricks that can be assembled in a water-tight manner (space-filling) to design a variety of spatial structures. Our approach takes inspiration from recently developed methods that utilize Voronoi tessellation of spatial domains by using symmetrically arranged Voronoi sites. However, in contrast to these existing methods, we focus our attention on Voronoi sites modeled using helical trajectories, which can provide corrugation and better interlocking. For symmetries, we only use affine transformations based on the Bravais lattice to avoid self-intersections. This methodology naturally results in structures that are both space-filling (owing to Voronoi tessellation) as well as interlocking by corrugation (owing to helical trajectories). The resulting shapes of the bricks appear to be similar to a variety of pasta noodles, thereby inspiring the names, Voronoi Spaghetti and VoroNoodles.