A. J. Kanel-Belov, A. V. Dyskin, Y. Estrin, E. Pasternak, I. A. Ivanov-Pogodaev, “Interlocking of convex polyhedra: towards a geometric theory of fragmented solids”, Mosc. Math. J., 10:2 (2010), 337

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Moscow Mathematical Journal, 2010, Volume 10, Number 2, Pages 337–342
DOI: https://doi.org/10.17323/1609-4514-2010-10-2-337-342 (Mi mmj383)

This article is cited in 34 scientific papers (total in 34 papers)

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

A. J. Kanel-Belov^abc, A. V. Dyskin^d, Y. Estrin^ef, E. Pasternak^g, I. A. Ivanov-Pogodaev^h

^a Moscow Institute of Open Education, Moscow, Russia
^b Department of Mathematics, Bar Ilan University, Ramat Gan, Israel
^c International University Bremen, Bremen, Germany
^d School of Civil and Resource Engineering, The University of Western Australia, Crawley, WA, Australia
^e ARC Centre of Excellence for Design in Light Metals, Department of Materials Engineering, Monash University, Clayton, Vic., Australia
^f CSIRO Division of Manufacturing and Materials Technology, Clayton, Vic., Australia
^g School of Mechanical Engineering, The University of Western Australia, Crawley, WA, Australia
^h Department of Mechanics and Mathematics, Moscow State University, Moscow, Russia

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DOI: https://doi.org/10.17323/1609-4514-2010-10-2-337-342

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.

Key words and phrases: interlocking structures, combinatorial geometry, convex polyhedron, tilling.

Received: November 7, 2006; in revised form January 7, 2007

Bibliographic databases:

Document Type: Article

MSC: 52B10, 74R

Language: English

Citation: A. J. Kanel-Belov, A. V. Dyskin, Y. Estrin, E. Pasternak, I. A. Ivanov-Pogodaev, “Interlocking of convex polyhedra: towards a geometric theory of fragmented solids”, Mosc. Math. J., 10:2 (2010), 337–342

Citation in format AMSBIB

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\paper Interlocking of convex polyhedra: towards a~geometric theory of fragmented solids

\jour Mosc. Math.~J.

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\vol 10

\issue 2

\pages 337--342

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Linking options:

https://www.mathnet.ru/eng/mmj383

https://www.mathnet.ru/eng/mmj/v10/i2/p337

This publication is cited in the following 34 articles:

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V. O. Manturov, A. Ya. Kanel-Belov, S. Kim, F. K. Nilov, “Two-Dimensional Self-Trapping Structures in Three-Dimensional Space”, Dokl. Math., 2024
Kheira Benyahia, Hichem Seriket, Sébastien Blanquer, Samuel Gomes, Mahdi Bodaghi, Jean-Claude André, Kun Zhou, H Jerry Qi, Frédéric Demoly, “Advancing 4D printing through designing interlocking blocks: enhancing deformation uniformity in active composite structures”, Smart Mater. Struct., 33:5 (2024), 055023
V. O. Manturova, A. Ya. Kanel-Belov, S. Kim, F. K. Nilov, “Two-dimensional self-trapping structures in three-dimensional space”, Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, 515:1 (2024), 92
Reymond Akpanya, Tom Goertzen, Alice C. Niemeyer, “From Tilings of Orientable Surfaces to Topological Interlocking Assemblies”, Applied Sciences, 14:16 (2024), 7276
Tom Goertzen, Domen Macek, Lukas Schnelle, Meike Weiß, Stefanie Reese, Hagen Holthusen, Alice C. Niemeyer, “Influence of block arrangement on mechanical performance in topological interlocking assemblies: A study of the versatile block”, International Journal of Solids and Structures, 2024, 113102
Tobias Neef, Tom Goertzen, Alice Niemeyer, Viktor Mechtcherine, “Materialsparende Betondecke aus 3D‐gedruckten Verriegelungsblöcken”, Beton und Stahlbetonbau, 2024
Estrin Yu., Beygelzimer Ya., Kulagin R., Gumbsch P., Fratzl P., Zhu Yu., Hahn H., “Architecturing Materials At Mesoscale: Some Current Trends”, Mater. Res. Lett., 9:10 (2021), 399–421
Estrin Yu., Krishnamurthy V.R., Akleman E., “Design of Architectured Materials Based on Topological and Geometrical Interlocking”, J. Mater. Res. Technol-JMRT, 15 (2021), 1165–1178
Wang Z., Song P., Pauly M., “State of the Art on Computational Design of Assemblies With Rigid Parts”, Comput. Graph. Forum, 40:2 (2021), 633–657
Aharoni L., Bachelet I., Carstensen V J., “Topology Optimization of Rigid Interlocking Assemblies”, Comput. Struct., 250 (2021), 106521
Williams A., Siegmund T., “Mechanics of Topologically Interlocked Material Systems Under Point Load: Archimedean and Laves Tiling”, Int. J. Mech. Sci., 190 (2021), 106016
Cornelie Leopold, Handbook of the Mathematics of the Arts and Sciences, 2021, 291
Vianney Loing, Olivier Baverel, Jean-François Caron, Romain Mesnil, “Free-form structures from topologically interlocking masonries”, Automation in Construction, 113 (2020), 103117
Casapulla C., Mousavian E., Zarghani M., “a Digital Tool to Design Structurally Feasible Semi-Circular Masonry Arches Composed of Interlocking Blocks”, Comput. Struct., 221 (2019), 111–126
Cornelie Leopold, Handbook of the Mathematics of the Arts and Sciences, 2019, 1
Cornelie Leopold, Handbook of the Mathematics of the Arts and Sciences, 2019, 1
Chao Gao, Josef Kiendl, “Short review on architectured materials with topological interlocking mechanisms”, Mat Design Process Comm, 1:1 (2019), e31
A. V. Dyskin, Yuri Estrin, E. Pasternak, Springer Series in Materials Science, 282, Architectured Materials in Nature and Engineering, 2019, 23
Zareiyan B., Khoshnevis B., “Effects of Interlocking on Interlayer Adhesion and Strength of Structures in 3D Printing of Concrete”, Autom. Constr., 83 (2017), 212–221

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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