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RISS 인기검색어
- 검색키워드
- 저자 : Rezaee Javan Anooshe (검색결과 2 건)
- 무료
- 기관 내 무료
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Dividing a sphere into equal-area and/or equilateral spherical polygons
Rezaee Javan Anooshe,Lee Ting-Uei,Xie Yi Min 한국CDE학회 2022 Journal of computational design and engineering Vol.9 No.2
Dividing a sphere uniformly into equal-area or equilateral spherical polygons is useful for a wide variety of practical applications. However, achieving such a uniform subdivision of a sphere is a challenging task. This study investigates two classes of sphere subdivisions through numerical approximation: (i) dividing a sphere into spherical polygons of equal area; and (ii) dividing a sphere into spherical polygons with a single length for all edges. A computational workflow is developed that proved to be efficient on the selected case studies. First, the subdivisions are obtained based on spheres initially composed of spherical quadrangles. New vertices are allowed to be created within the initial segments to generate subcomponents. This approach offers new opportunities to control the area and edge length of generated subdivided spherical polygons through the free movement of distributed points within the initial segments without restricting the boundary points. A series of examples are presented in this work to demonstrate that the proposed approach can effectively obtain a range of equal-area or equilateral spherical quadrilateral subdivisions. It is found that creating gaps between initial subdivided segments enables the generation of equilateral spherical quadrangles. Secondly, this study examines spherical pentagonal and Goldberg polyhedral subdivisions for equal area and/or equal edge length. In the spherical pentagonal subdivision, gaps on the sphere are not required to achieve equal edge length. Besides, there is much flexibility in obtaining either the equal area or equilateral geometry in the spherical Goldberg polyhedral subdivisions. Thirdly, this study has discovered two novel Goldberg spherical subdivisions that simultaneously exhibit equal area and equal edge length.
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New families of cage-like structures based on Goldberg polyhedra with non-isolated pentagons
Rezaee Javan Anooshe,Liu Yuanpeng,Xie Yi Min 한국CDE학회 2023 Journal of computational design and engineering Vol.10 No.2
A Goldberg polyhedron is a convex polyhedron made of hexagons and pentagons that have icosahedral rotational symmetry. Goldberg polyhedra have appeared frequently in art, architecture, and engineering. Some carbon fullerenes, inorganic cages, viruses, and proteins in nature exhibit the fundamental shapes of Goldberg polyhedra. According to Euler’s polyhedron formula, an icosahedral Goldberg polyhedron always has exactly 12 pentagons. In Goldberg polyhedra, all pentagons are surrounded by hexagons only—this is known as the isolated pentagon rule (IPR). This study systematically developed new families of cage-like structures derived from the initial topology of Goldberg polyhedra but with the 12 pentagons fused in five different arrangements and different densities of hexagonal faces. These families might be of great significance in biology and chemistry, where some non-IPR fullerenes have been created recently with chemical reactivity and properties markedly different from IPR fullerenes. Furthermore, this study has conducted an optimization for multiple objectives and constraints, such as equal edge length, equal area, planarity, and spherical shape. The optimized configurations are highly desirable for architectural applications, where a structure with a small number of different edge lengths and planar faces may significantly reduce the fabrication cost and enable the construction of surfaces with flat panels.
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