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

A. Belov; A.V. Dyskin; Y. Esrin; E. Pasternak; I.A. Ivanov

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

A. Belov, A.V. Dyskin, Y. Esrin, E. Pasternak, I.A. Ivanov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Abstract. 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. 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. Glickman and were not described in mathematical publications. The full version of this paper is presented here: http://arxiv.org/abs/0812.5089.

Original language	American English
Pages (from-to)	337-342
Journal	Moscow Mathematical Journal
Volume	10
Issue number	2
State	Published - 2010

Cite this

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title = "Interlocking of convex polyhedra: towards a geometric theory of fragmented solids",

abstract = "Abstract. 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. 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. Glickman and were not described in mathematical publications. The full version of this paper is presented here: http://arxiv.org/abs/0812.5089.",

author = "A. Belov and A.V. Dyskin and Y. Esrin and E. Pasternak and I.A. Ivanov",

year = "2010",

language = "American English",

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pages = "337--342",

journal = "Moscow Mathematical Journal",

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publisher = "Independent University of Moscow",

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T1 - Interlocking of convex polyhedra: towards a geometric theory of fragmented solids

AU - Belov, A.

AU - Dyskin, A.V.

AU - Esrin, Y.

AU - Pasternak, E.

AU - Ivanov, I.A.

PY - 2010

Y1 - 2010

N2 - Abstract. 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. 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. Glickman and were not described in mathematical publications. The full version of this paper is presented here: http://arxiv.org/abs/0812.5089.

AB - Abstract. 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. 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. Glickman and were not described in mathematical publications. The full version of this paper is presented here: http://arxiv.org/abs/0812.5089.

UR - http://www.ams.org/distribution/mmj/vol10-2-2010/kanel-belov-etal.pdf

M3 - Article

SN - 1609-3321

VL - 10

SP - 337

EP - 342

JO - Moscow Mathematical Journal

JF - Moscow Mathematical Journal

IS - 2

ER -

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

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