%0 Journal Article
%T Interlocking of convex polyhedra: towards a geometric theory of fragmented solids
%A A. J. Kanel-Belov
%A A. V. Dyskin
%A Y. Estrin
%A E. Pasternak
%A I. A. Ivanov-Pogodaev
%J Mathematics
%D 2008
%I arXiv
%X We present structures comprised of identical convex polyhedra which are interlocked geometrically. These sets cannot be disassembled by removing individual polyhedra by translations and/or rotations. The shapes that permit interlocking arrangements include all five platonic solids. Criteria for interlocking based on transformations of the cross-sections of the elements in a 3D reconstruction of a layer from its middle cross-section are formulated. A generalization to higher dimensions is also given. In particular, an interlocking layer of four-dimensional cubes is described.
%U http://arxiv.org/abs/0812.5089v1