Self-interlocking structures in $R^2$ and $R^3$

Consider a set of contacting convex figures in $R^2$. It can be proven that one of these figures can be moved out of the set by translation without disturbing others. Therefore, any set of planar figures can be disassembled by moving all figures one by one. However, attempts to generalize it to $R^3$ have been unsuccessful and quite unexpectedly interlocking structures of convex bodies were found. Author proposed the following mechanical use of this effect. In a small grain there is no room for cracks, and crack propagation should be arrested on the boundary of the grain. On the other hand, grains keep each other. So it is possible to get "materials without crack propagation" and get new use of sparse materials, say ceramics. Quite unexpectedly, such structures can be assembled with any type of platonic polyhedra, and they have a geometric beauty. Some patents were obtained