Applications of aesthetic pentagon-shaped stereo tiling employing pentagraphene carbon—star walls and embossment design

Abstract

A three-dimensional pentagon-shaped stereo-tiling concept has been realized through use of penta-graphene carbon structures, although mathematically, regular planar pentagon shapes cannot be used to completely tile the Euclidean plane. Two applications of the findings of this study have been considered from the mathematical and engineering viewpoints. First, the proposed discovery facilitates math-rule-based generation of beautiful designs comprising star shapes formed using regular pentagons. The underlying mathematical logic and hexagon-division rules have been deduced to obtain the proposed pentagonal stereo-tiling pattern comprising equal-length bonds, and two aesthetic designs have been derived using the deduced logic. A fence-like structure exclusively comprising pentagram stars has been designed and given the name “Star Walls.” Emphasis has also been laid on application of the proposed stereo-tiling concept in industrial design operations, such as emboss manufacturing. To this end, finite element analysis of embossed steel sheets has been performed to verify the feasibility of the said industrial application.