Polygonal tiling: Periodic and aperiodic and some other related mathematical concepts



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My current research investigates one and two-dimensional tiling. This thesis will discuss two major categories, periodic and aperiodic tiling, as well as, tiling patterns of many different types and structures. Initially, I will define periodic tiling as a process of decomposing the flat surface into numerous small polygonal tiles arranged into a lattice with the condition that there be no gaps or overlaps. Regular tiling can satisfy the condition. However, a polygon of more than six sides cannot tile the plane nor can a regular pentagon. Additionally, there are 11 distinct types of semi-regular tilings and 20 different kinds of 2-uniform tiling that would reveal periodicity. Aperiodic, by contrast, is a tiling with no repetition. Each type of aperiodic tiling is distinct. The second major part of this work will discuss pattern in variant types and structures. The final chapter investigates the importance of motifs. The motivation for the study of artistic motifs in tiling was the desire to revive this unique decorative art in contemporary practice of interior design and architecture in our buildings.



Polygonal tiling, Periodic, Aperiodic, Pattern, Semi-regular, 2-uniform tiling, Rosette, Frieze, Wallpaper, Quasi-crystal, Crystallography