Topologically Interlocking Blocks Inside the Tetroctahedrille

Abstract A topological interlocking assembly (TIA) consists of rigid blocks together with a fixed frame, such that all blocks are kinematically constrained and can therefore not be removed from the assembly. In recent years, these assemblies have gained a lot of interest due to their suitability for the construction of sustainable modular systems. We pursue a modular approach to construct interlocking blocks by exploiting the tetroctahedrille. This leads to the discovery of two interlocking blocks, which we call kitten and UFO, whose corresponding TIAs realise spiral forms. We show that given TIAs can be deformed continuously in order to obtain new TIAs. We also present a geometric application of the tetroctahedrille for approximating given geometric objects. Additionally, we discuss how physical models with incorporated magnets can be employed to motivate the construction of such geometries with special application in civil engineering.