  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.
