Topological Interlocking, Truchet Tiles and Self-Assemblies: A Construction-Kit for Civil Engineering Design

Topological interlocking is an abstract concept which requires that, given an assembly of blocks with a fixed frame as a constraint, no group of blocks can be removed. We introduce a construction kit based on a block, called Versatile Block, that leads to a wide range of possible topological interlocking assemblies. We show that the combinatorics of assembling copies of this block can be linked to Truchet tiles. We analyze the self assembly behaviour of the block
by presenting experimental results based on 3D-printing with inserted magnets and computational experiments using the computer algebra system GAP. Furthermore, we present structural examples demonstrating the functionalities of each block in the construction kit. We investigate different design strategies and discuss possible applications in civil engineering design, considering possible manufacturing with different choices of material such as carbon reinforced
concrete.