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Mosc. Math. J., 2010, Volume 10, Number 2, Pages 337–342 (Mi mmj383)  

This article is cited in 13 scientific papers (total in 13 papers)

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

A. J. Kanel-Belovabc, A. V. Dyskind, Y. Estrinef, E. Pasternakg, I. A. Ivanov-Pogodaevh

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

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:

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


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MSC: 52B10, 74R
Received: November 7, 2006; in revised form January 7, 2007

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
\by A.~J.~Kanel-Belov, A.~V.~Dyskin, Y.~Estrin, E.~Pasternak, I.~A.~Ivanov-Pogodaev
\paper Interlocking of convex polyhedra: towards a~geometric theory of fragmented solids
\jour Mosc. Math.~J.
\yr 2010
\vol 10
\issue 2
\pages 337--342

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    This publication is cited in the following articles:
    1. Estrin Yu., Dyskin A., Pasternak E., Schaare S., “Topological interlocking in design of structures and materials”, Architecture multifunctional materials, Materials Research Society Symposium Proceedings, 1188, 2009, 117–129  crossref  isi
    2. Estrin Y., Dyskin A.V., Pasternak E., “Topological interlocking as a material design concept”, Materials Science & Engineering C-Materials for Biological Applications, 31:6 (2011), 1189–1194  crossref  isi  scopus
    3. Li J., Xue J., Xiao J., Wang Y., “Block theory on the complex combinations of free planes”, Computers and Geotechnics, 40 (2012), 127–134  crossref  isi  scopus
    4. Molotnikov A., Gerbrand R., Bouaziz O., Estrin Yu., “Sandwich Panels with a Core Segmented Into Topologically Interlocked Elements”, Adv. Eng. Mater., 15:8 (2013), 728–731  crossref  isi  elib  scopus
    5. Dyskin A.V., Pasternak E., Shufrin I., “Structure of Resonances and Formation of Stationary Points in Symmetrical Chains of Bilinear Oscillators”, J. Sound Vibr., 333:24 (2014), 6590–6606  crossref  isi  elib  scopus
    6. Li J., Yuan G., Zhang Yu., Zhao Ya., “Study on a General Cutting Algorithm of Complex Blocks”, Geotech. Geol. Eng., 33:5 (2015), 1193–1203  crossref  isi  elib  scopus
    7. Zheng Yinhe, Xia Lu, Yu Qingchun, “a Method For Identifying Three-Dimensional Rock Blocks Formed By Curved Fractures”, Comput. Geotech., 65 (2015), 1–11  crossref  isi  elib  scopus
    8. Molotnikov A., Gerbrand R., Qi Y., Simon G.P., Estrin Y., “Design of Responsive Materials Using Topologically Interlocked Elements”, Smart Mater. Struct., 24:2 (2015), 025034  crossref  isi  elib  scopus
    9. Siegmund T., Barthelat F., Cipra R., Habtour E., Riddick J., “Manufacture and Mechanics of Topologically Interlocked Material Assemblies”, Appl. Mech. Rev., 68:4 (2016), 040803  crossref  isi  scopus
    10. Djumas L., Molotnikov A., Simon G.P., Estrin Yu., “Enhanced Mechanical Performance of Bio-Inspired Hybrid Structures Utilising Topological Interlocking Geometry”, Sci Rep, 6 (2016), 26706  crossref  isi  scopus
    11. 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  crossref  isi  scopus
    12. Djumas L., Simon G.P., Estrin Yu., Molotnikov A., “Deformation Mechanics of Non-Planar Topologically Interlocked Assemblies With Structural Hierarchy and Varying Geometry”, Sci Rep, 7 (2017), 11844  crossref  isi  scopus
    13. Piirainen V.Y., Estrin Y.Z., “Topological Interlocking as a Principle of Engineering Design in Consruction of Marine and Coastal Structures”, J. Min. Inst., 226 (2017), 480–486  isi
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