Topologically Interlocking Blocks Inside the Tetroctahedrille

Nexus Network Journal, vol. 28, pp. 1005–1023

Abstract

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.

Authors 3

1. Reymond Akpanya corresponding

   The University of Sydney

   Affiliation as printed

   School of Mathematics and Statistics, University of Sydney, Sydney, Australia

2. Tom Goertzen

   The University of Sydney

   Affiliation as printed

   School of Mathematics and Statistics, University of Sydney, Sydney, Australia

3. Alice C. Niemeyer Aachen Chair of Algebra and Representation Theory

   RWTH Aachen University

   Affiliation as printed

   Chair of Algebra and Representation Theory, RWTH Aachen University, Aachen, Germany