The Number of Boundary H-points of Convex H-quadrilateral  

凸H-四边形的边界H-点数

作　　者：WEI Xianglin ZHU Weili 魏祥林;朱伟丽(河北科技大学理学院,河北石家庄050014)

机构地区：[1]College of Science,Hebei University of Science and Technology,Shijiazhuang,Hebei,050018,P.R.China

出　　处：《数学进展》2025年第1期177-186,共10页Advances in Mathematics(China)

基　　金：Supported by NSFC(No.12271139)。

摘　　要：An H-polygon is a polygon with corners in the set of vertices of a tiling of R~2 by regular hexagons of unit edge.It is known that any H-triangle with exactly k interior H-points can have at most 3k+7 boundary H-points.In this note we prove that any convex H-quadrilateral with exactly k interior H-points can have at most 3k+7 boundary H-points.H-多边形是以边长为一的正六边形平面铺砌顶点集上的点为顶点的多边形.已经知道内部包含k个H-点的H-三角形至多能有3k+7个边界H-点.本文证明此结论对凸H-四边形也是成立的,即内部包含k个H-点的任意凸H-四边形至多包含3k+7个边界H-点.

关 键 词：discrete geometry regular hexagonal tiling H-quadrilateral H-point 

分 类 号：O157.3[理学—数学]