Abstract
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.
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Vörös, L. (2019). Geometrical Structures of Planar and Spatial Tessellations Based on 3D Models of Higher Dimensional Cubes. In: Cocchiarella, L. (eds) ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics. ICGG 2018. Advances in Intelligent Systems and Computing, vol 809. Springer, Cham. https://doi.org/10.1007/978-3-319-95588-9_38
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DOI: https://doi.org/10.1007/978-3-319-95588-9_38
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