# Interlocking Structures

Consider a set of 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 the 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 finally,

quite unexpectedly, interlocking structures of convex bodies were

found. These structures can be used in engineering. 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. Surprisingly, such

structures can be assembled with any type of platonic polyhedra, and

they have a geometric beauty.

- Last modified: 6/06/2018