LDP quadrilaterals with Gorenstein index at most 500

This record contains all LDP quadrilaterals (lattice triangles with primitive vertices and origin in their interior) up to Gorenstein index \( 500 \). Equivalently, these are the toric del Pezzo surfaces with Gorenstein index at most \( 500 \). We use the HDF5 file format to store them. The quadrilaterals have been obtained using RationalPolygons.jl. Structure of the HDF5 file In the HDF5 file, the quadrilaterals are split into different datasets according to their Gorenstein index. We use "gi" to denote the Picard index. For example, the triangles with Gorenstein index \(12\) are located in the dataset "/gi12". Each dataset of quadrilaterals is one-dimensional with one entry per quadrilateral. A quadrilateral is stored using a compound datatype with \(8\) fields of integers. These integers are the vertices of the quadrilateral stored in column major layout. For example, a quadrilateral with vertices \((x_1,y_1), (x_2,y_2), (x_3, y_3)\) and \((x_4,y_4)\) is stored as the tuple \((x_1,y_1,x_2,y_2,x_3,y_3,x_4,y_4)\). Moreover, the file contains the special dataset "numbers_of_polygons" that stores the numbers of quadrilaterals for each Gorenstein index.