A Topological Interlocking Configuration (TIC), from a geometric point of view, is an assembly of building blocks that is stable without fasteners or adhesives of any kind. Stability is achieved by the geometry of the contact interfaces of the building blocks. The fundamental concepts regarding the construction of such configurations as well as their geometric interlocking attributes have been formulated in (Kanel-Belov, 2008). Different TICs based on semi-regular tessellations of the plane and of curvilinear surfaces using polyhedra other than the Platonic solids are described in (Weizmann, 2017), (Weizmann, 2016) and (Weizmann, 2015). We propose a method that generates cylindrical TICs using both regular tetrahedra and quasi tetrahedra pieces. The method differs from the traditional TIC generation approach.