Interior Hulls of Clean Lattice Parallelograms and Continued Fractions

The interior hull of a lattice polygon is the convex closure of the lattice points in the interior of the polygon. In this paper we give a concrete description of the interior hull of a clean lattice parallelogram. A clean parallelogram in ℝ^2 is a lattice parallelogram whose boundary contains no lattice points other than its vertices. Using unimodular maps we can identify a clean parallelogram with a parallelogram, P_a,n, whose vertices are (0,0), (1,0), (a,n) and (a+1,n), with 0More