Topologically Interlocking Blocks inside the Tetroctahedrille

TL;DR

This paper introduces a modular method for constructing topologically interlocking blocks using tetrahedra and octahedra based on the tetroctahedrille honeycomb, enabling versatile assemblies and geometric approximations.

Contribution

It presents a novel modular approach to create non-convex interlocking blocks from tetrahedra and octahedra, expanding the design possibilities for topological assemblies.

Findings

Versatile interlocking blocks based on tetroctahedrille

Construction of families of interlocking blocks

Application in geometric approximation

Abstract

A topological interlocking assembly consists of rigid blocks together with a fixed frame, such that any subset of blocks is kinematically constrained and therefore cannot be removed from the assembly. In this paper we pursue a modular approach to construct (non-convex) interlocking blocks by combining finitely many tetrahedra and octahedra. This gives rise to polyhedra whose vertices can be described by the tetrahedral-octahedral honeycomb, also known as tetroctahedrille. We show that the resulting interlocking blocks are very versatile and allow many possibilities to form topological interlocking assemblies consisting of copies of a single block. We formulate a generalised construction of some of the introduced blocks to construct families of topological interlocking blocks. Moreover, we demonstrate a geometric application by using the tetroctahedrille to approximate given geometric objects. Finally, we show that given topological interlocking assemblies can be deformed continuously in order to obtain new topological interlocking assemblies.