Convex Lattice Heptagons with Boundary Trapezoids

Abstract

We consider a Cartesian coordinate system. A point in a plane whose both coordinates are integers is called a lattice point. A polygon that has lattice points for all its vertices is called a convex lattice polygon. A quadrilateral whose vertices are four consecutive vertices of a convex integer polygon is called a boundary quadrilateral of that polygon. It is interesting to investigate convex lattice polygons whose all boundary quadrilaterals are trapezoids.