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As shown by McMullen in 1983, the coefficients of the Ehrhart polynomial of alattice polytope can be written as a weighted sum of facial volumes. Theweights in such a local formula depend only on the outer normal cones of faces,but are far from being unique. In this paper, we develop an infinite class ofsuch local formulas. These are based on choices of fundamental domains insublattices and obtained by polyhedral volume computations. We hereby also givea kind of geometric interpretation for the Ehrhart coefficients. Since ourconstruction gives us a great variety of possible local formulas, these can,for instance, be chosen to fit well with a given polyhedral symmetry group. Incontrast to other constructions of local formulas, ours does not rely ontriangulations of rational cones into simplicial or even unimodular ones.

Local Formulas for Ehrhart Coefficients from Lattice Tiles