Lattice polygons with at most 70 lattice points

This record contains all lattice polygons with at most 70 lattice points. The algorithm to classify them is due to Koelman, see section 4.4 of his dissertation (reference below). His original classification was up to 42 lattice points, but his data was not publicily available. We have implemented his algorithm in RationalPolygons.jl, recreating and extending his classification. Structure of the HDF5 files The data is contained in a single tar archive "koelman70.tgz", which contains files l3.h5, l4.h5, ... l70.h5 storing the polygons with given number of lattice points. We use the HDF5 file format. In the HDF5 files, the polygons are split into different datasets according to their number of vertices, which we denote by "n". There is one dataset for every number of vertices. For example, the lattice polygons with 6 vertices having 50 lattice points are located in "l50.h5" under the dataset "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 multiplied by two, 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 \((2\cdot x_1,2\cdot y_1,2 \cdot x_2,2\cdot y_2,2 \cdot x_3,2 \cdot y_3)\). Moreover, each file contains the special one-dimensional dataset "numbers_of_polygons" that stores the numbers of polygons for given number of vertices.