Geometrical Structures of Planar and Spatial Tessellations Based on 3D Models of Higher Dimensional Cubes

  • László VörösEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 809)


A special 3-dimensional model of more-dimensional cubes is described in the paper. The parts of this are 3D models of the lower-dimensional elements of the cube. These have rhombic faces that are congruent with the faces of the model of the whole cube. The suitable combinations of all these elements touching each other by the congruent faces create periodical space-filling tessellations. The spatial mosaics gained this way can have helical and fractal or fractal like structures after different reconstructions. The planar intersections of the spatial tessellations provide series of plane-tiling patterns that can be also restructured in order to have more sophisticated mosaics. The topic can have relations to industry, arts and design. Some new constructions are described and showed by figures in the paper and animations of the gained patterns are viewable on a referred home page.


Constructive geometry Hypercube modelling Planar and spatial tessellation Fractal Design 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.University of PécsPécsHungary

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