Construction Methods for Space-Filling Heterogeneous Topological Interlocking Assemblies

TL;DR

This paper introduces systematic construction methods for space-filling topological interlocking assemblies using wallpaper groups and tessellations, expanding design possibilities for architectural and material applications.

Contribution

It presents novel construction techniques for TIAs that fill space between parallel planes with multiple block types, including generalized Truchet tiles and lozenge tilings.

Findings

Constructed TIAs fully occupy space between two parallel planes.

Established correspondence between tilings and specific TIAs.

Expanded the design space for interlocking systems.

Abstract

Deforming fundamental domains of wallpaper groups provides a systematic way to generate non-convex blocks which admit topological interlocking assemblies (TIAs). We use this approach to construct TIAs that fully occupy the space between two parallel planes and incorporate multiple block types. In addition to wallpaper groups, semiregular tessellations are employed in the construction of such TIAs. These construction methods open up an extensive design space for TIAs, expanding the possibilities of feasible interlocking systems and creating new opportunities for architectural and material design. Several resulting block families can be interpreted as geometric realizations of generalized Truchet tiles or decorated lozenge tilings and, with suitable colouring rules, we establish a one-to-one correspondence between these tilings and specific TIAs. This framework enables a systematic investigation of symmetric and asymmetric assemblies derived from diverse block types.