Lattice polygons with at most 70 lattice points

This record contains All lattice polygons with at most 70 lattice points, All interior lattice polygons with at most 112 lattice points, where a lattice polygon is called interior if it is the convex hull of interior lattice points of another lattice polygon. The algorithm to classify lattice polygons by lattice points 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 two archives "koelman70.tgz" and "koelman_interiors112.tgz" contain files l3.h5, l4.h5, etc... storing the polygons with given number of lattice points in 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, which are the vertices of the polygon. 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 one-dimensional dataset "numbers_of_polygons" that stores the numbers of polygons for given number of vertices.