Interlocking of Convex Polyhedra: towards a Geometric Theory of Fragmented Solids

What is it about?

The article presents arrangements of identical regular polyhedra with very special and curious properties. Namely, the solids are situated in a sort of a layer and are interlocked in the sense that no one of them can be moved out without disturbing others. This situation cannot happen in the plane. The first examples of this sort (composed of irregular convex polyhedra) were complicated and were constructed in a non-regular way by G. Galperin. The examples presented here were constructed in the framework of applied studies by the authors, C. Khor and M. Glickman, and were not described in mathematical publications. The full version of this paper is available at arxiv.org/abs/0812.5089.

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