Lindner, MarkoMarkoLindnerRoch, SteffenSteffenRoch2021-10-252021-10-252010-06-10arXiv: 1006.2053 (2021)http://hdl.handle.net/11420/10572In this article we compare the set of integer points in the homothetic copy nΠ of a lattice polytope Π⊆ᵈ with the set of all sums x₁+⋯+xn with x₁,...,xn∈ Π∩ᵈ and n∈. We give conditions on the polytope Π under which these two sets coincide and we discuss two notions of boundary for subsets of ᵈ or, more generally, subsets of a finitely generated discrete group.enMetric GeometryNumerical AnalysisMathematikPreprint10.48550/arXiv.1006.20531006.2053Preprint