Special hypercube models and 3d-tessellations based on five cubes joining the vertices of the platonic dodecahedron

Vörös, László (2018) Special hypercube models and 3d-tessellations based on five cubes joining the vertices of the platonic dodecahedron. Pollack Periodica, 13 (1). pp. 225-236. ISSN 1788-1994

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Abstract

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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