Pollack Periodica
Volume/Issue:
Volume 13: Issue 1
Special hypercube models and 3d-tessellations based on five cubes joining the vertices of the platonic dodecahedron
Author: László Vörös 1
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  • 1 Faculty of Engineering and Information Technology, University of Pécs, Boszorkány út 2, H-7624 Pécs, Hungary
DOI:
https://doi.org/10.1556/606.2018.13.1.20
Page Count:
225–236
Publication Date:
01 Apr 2018
Online Publication Date:
Apr 2018
Open access

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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    Fenyvesi K. Bridges: A world community for mathematical art, The Mathematical Intelligencer, Vol. 38, No. 2, 2016, pp. 35–45.
Cover Pollack Periodica
Pollack Periodica
Print ISSN:
1788-1994
Online ISSN:
1788-3911
Keywords:
Platonic and Archimedean solid; Hypercube model; Spatial and planar tessellations

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