Topological interlocking of platonic solids: a way to new materials and structures

The structural integrity of natural and engineered materials relies on chemical or mechanical bonding between the building blocks of which they consist. Materials whose building blocks are not joined, but rather interlocked topologically, possess remarkable mechanical and functional properties. We show that identical elements, in the shape of the five platonic solids, can be arranged into layer-like structures in which they are interlocked topologically. It is shown that truncated icosahedra (buckyballs) can also be arranged in a layer with topological interlocking. The geometrical possibility of such assemblies opens up interesting avenues in the design of structures and materials.