Lattice subpolygons of a square with given sidelength

This record contains all lattice subpolygons of the square of sidelength \(m\) for \(1 \leq m \leq 10\). There is one file for each sidelength. We use the HDF5 file format to store the polygons. The polygons have been obtained using RationalPolygons.jl. Structure of the HDF5 files In each file, the polygons are split into different datasets according to their normalized area and number of vertices. We use "a" to denote the normalized area (twice the euclidian area) and "n" to denote the number of vertices. For example, the subpolygons of the square of sidelength \(4\) with normalized area \(20\) having \(6\) vertices are located in "m4.h5" under the dataset "/a20/n6". Each dataset of polygons is one-dimensional with one entry per polygon. A polygon is stored using a compound datatype with \(2 \cdot n\) fields of integers. These integers are the vertices of the polygon stored in column major layout. For example, a triangle with vertices \((x_1,y_1), (x_2,y_2)\) and \((x_3,y_3)\) is stored as the tuple \((x_1,y_1,x_2,y_2,x_3,y_3)\). Moreover, each file contains the special two-dimensional dataset "numbers_of_polygons" that stores the numbers of polygons for a given normalized volume and number of vertices.本数据集包含边长为(m)（(1 leq m leq 10)）的正方形的所有格点子多边形。每个边长对应一个单独文件，采用HDF5（Hierarchical Data Format 5）文件格式存储多边形。所有多边形均通过RationalPolygons.jl生成。 HDF5文件结构说明： 在每个文件中，多边形将按照其归一化面积与顶点数量划分至不同数据集。我们以“a”指代归一化面积（即两倍欧几里得面积），以“n”指代顶点数量。例如，边长为4的正方形中，归一化面积为20且包含6个顶点的子多边形，存储于文件“m4.h5”的数据集路径`/a20/n6`下。每个多边形数据集为一维数组，每个元素对应一个多边形。多边形采用包含(2 cdot n)个整数字段的复合数据类型存储，这些整数按列主序布局依次存储多边形的顶点坐标。例如，顶点为((x_1,y_1), (x_2,y_2), (x_3,y_3))的三角形，将以元组((x_1,y_1,x_2,y_2,x_3,y_3))的形式存储。此外，每个文件还包含一个特殊的二维数据集“numbers_of_polygons”，用于存储给定归一化面积与顶点数量对应的多边形总数量。