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

A. J. Kanel-Belov, A. V. Dyskin, Y. Estrin, E. Pasternak, I. A. Ivanov-Pogodaev

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29 Scopus citations


The article presents arrangements of identical regular poly-hedra 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. 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 framework of applied studies by the authors, C. Khor and M. Glick-man and were not described in mathematical publications. The full version of this paper is presented here:

Original languageEnglish
Pages (from-to)337-342
Number of pages6
JournalMoscow Mathematical Journal
Issue number2
StatePublished - 2010


  • Combinatorial geometry
  • Convex polyhedron
  • Interlocking structures
  • Tilling


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