Geodesic
Convex hulls of integral points
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Tome 266 (2000), pp. 188-217

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The convex hull of all integral points contained in a compact polyhedron $C$ is obviously a compact polyhedron. When $C$ is not compact, the convex hull $K$ of its integral points need not be a closed set. However under some natural assumptions, $K$ is a closed set and a generalized polyhedron. 
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     author = {J.-O. Moussafir},
     title = {Convex hulls of integral points},
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J.-O. Moussafir. Convex hulls of integral points. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Tome 266 (2000), pp. 188-217. http://geodesic.mathdoc.fr/item/ZNSL_2000_266_a11/