Author(s)

PeiChang Ouyang^*, Yan Lin, LiHua Liu

Affiliation(s)

School of Science, Guangxi University of Science and Technology, Liuzhou 545006, Guangxi, China.

Corresponding Author

PeiChang Ouyang

ABSTRACT

The field of planar tiling has captivated mathematicians, artists, and architects for centuries, driven by the desire to create intricate and harmonious patterns. Recent advancements have focused on developing new methods and technologies for constructing these patterns, particularly with the advent of advanced manufacturing and computational tools. This paper introduces a novel approach utilizing planar polyhedral tiles with interlocking elements to construct a wide range of two-dimensional symmetry structures. Based on the principles of fundamental domains in finite reflection groups, this technology allows for the creation of complex and aesthetically pleasing patterns. The tiles are designed to fit together perfectly, forming a dense packing that covers the entire plane without gaps or overlaps. The interlocking elements ensure stability and enable the creation of structures exhibiting high degrees of symmetry and order. This innovation has significant implications not only for traditional fields such as architecture and design but also for materials science and engineering, where it offers new possibilities for creating lightweight, strong composites and improving surface properties. The potential applications of this technology are vast, promising to revolutionize various industries and push the boundaries of creativity and functionality.

KEYWORDS

Tiling; Symmetry group; Reflection group; Fundamental region; CAD

CITE THIS PAPER

PeiChang Ouyang, Yan Lin, LiHua Liu. Plannar interlocking tilings based on finite reflection groups. Educational Research and Human Development. 2025, 2(1): 1-7. DOI: https://doi.org/10.61784/erhd3026.

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