Interlocking of convex polyhedra: towards a geometric theory of fragmented solids

Details Interlocking of convex polyhedra: towards a geometric theory of fragmented solids Interlocking of convex polyhedra: towards a geometric theory of fragmented solids

2008-12-30

arxiv.org/abs/0812.5089v1

Mathematics

Metric Geometry

15 pages, 11 figures

Scientific paper

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.

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