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  • 1 Faculty of Engineering and Information Technology, University of Pécs, Boszorkány út 2, H-7624 Pécs, Hungary

The 3-dimensional model of any k-dimensional cube can be constructed by starting k edges whose Minkowski sum can be called zonotope. Combined 2<j<k initial edges result in 3-models of j-cubes as parts of a k-cube. Suitable combinations of these zonotopes result in 3-dimensional space-filling mosaics. The base of the described cases, presented here, is five cubes constructed with joining vertices in the Platonic dodecahedron. These have 15 differently directed edges whose above zonotope is the 3-model of the 15-cube, or the Archimedean truncated icosidodecahedron. The reported further zonotopes are 3-models of lower-dimensional parts of this one. Pedagogical aspects of this topic are also emphasized.

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  • [1]

    Vörös L. Two new space-filling mosaics based on a symmetric 3D model of the 10D cube, Pollack Periodica, Vol. 11, No. 1, 2016, pp. 8190.

    • Search Google Scholar
    • Export Citation
  • [2]

    Vörös L. Structures in the space of Platonic and Archimedean solids, Serbian Architectural Journal, Structural Systems, Vol. 3, No. 2, 2011, pp. 140151.

    • Search Google Scholar
    • Export Citation
  • [3]

    Vörös L. http://geometria.mik.pte.hu/videok.html, video 21.1-5 (last visited 3 July 2017).

  • [4]

    Coxeter H. S. M. Regular polytopes, 2nd ed, The MacMillan Company, New York, 1963.

  • [5]

    Towle R. Zonotopes, symmetrical-structures, 2008, http://zonotopia.blogspot.com (last visited 3 July 2017).

  • [6]

    Vörös L. Reguläre Körper und mehrdimensionale Würfel, KoG Scientific and Professional Journal of the Croatian Society for Geometry and Graphics, No. 9, 2005, pp. 2127, http://master.grad.hr/hdgg/kog_stranica/kog9.pdf (last visited 3 July 2017).

    • Search Google Scholar
    • Export Citation
  • [7]

    Grünbaum, B. Uniform tilings of 3-space, Geombinatorics, 1994, Vol. IV, No. 2, pp. 4956.

  • [8]

    Vörös L. Specialties of models of the 6-dimensional cube, Proceedings of Bridges, 2010, Mathematics, Music, Art, Architecture, Culture, Pécs, Hungary, 24-28 July 2010, pp. 353358.

    • Search Google Scholar
    • Export Citation
  • [9]

    Experience Workshop, http://www.elmenymuhely.hu/?lang=en (last visited 3 July 2017).

  • [10]

    Fenyvesi K. Bridges: A world community for mathematical art, The Mathematical Intelligencer, Vol. 38, No. 2, 2016, pp. 3545.

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