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内含k个H-点且边界H-点数为3k+5的H-三角形 被引量:1

H-triangle with k interior H-points and 3k+5 boundary H-points
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摘要 为了研究内含k个H-点的H-多边形的边界特性和几何结构,针对正六边形阿基米德铺砌,研究铺砌上的H-三角形内部H-点和边界H-点的关系。首先,通过分析H-三角形的三元组(α,β,γ),确定所有可能满足要求的三元组;其次,利用位级线理论和铺砌点分布特性,排除不能实现的三元组;最后,证明内含k个H-点且边界H-点数为3k+5的H-三角形存在,且只有2种构图,并给出这2种构图的具体构造。结果表明,在能够确定三角形所有可能的三元组条件下,H-三角形满足给定边界点数的图形结构是确定的。研究结果丰富了阿基米德铺砌的相关理论,也为阿基米德铺砌相关问题的研究提供了重要的理论依据。 In order to study the boundary characteristics and geometric structure of an H-polygon with k interior H-points,the relationship between the interior H-points and boundary H-points of the H-triangle in a regular hexagonal Archimedean tiling was studied.Firstly,by analyzing the triple(α,β,γ)of H-triangle,the triples that may meet the requirements were determined.Then,the impossible triples were excluded by using the theory of level and the distribution characteristics of tiling points.Finally,H-triangle with k interior H-points and 3k+5 boundary H-points was obtained.Considering there were only two types of configurations,the specific constructions of these two configurations were given.The results show that the configurations of the H-triangle which satisfies the given number of boundary H-points are certain under the condition that all possible triples of triangle can be determined.The research results enrich the related theories of Archimedean tiling,and provide an important theoretical basis for the research of related problems of Archimedean tiling.
作者 朱伟丽 魏祥林 ZHU Weili;WEI Xianglin(School of Sciences,Hebei University of Science and Technology,Shijiazhuang,Hebei 050018,China)
出处 《河北科技大学学报》 CAS 北大核心 2023年第2期144-151,共8页 Journal of Hebei University of Science and Technology
基金 国家自然科学基金(11871192,12271139)。
关键词 离散数学 离散几何 阿基米德铺砌 正六边形铺砌 H-三角形 H-点 discrete mathematics discrete geometry Archimedean tiling regular hexagonal tiling H-triangle H-point
作者简介 第一作者简介:朱伟丽(1998-),女,河北石家庄人,硕士研究生,主要从事离散与组合几何方面的研究。;通信作者:魏祥林,教授。E-mail:sd_wxl@126.com。
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