Perfect prismatoids are lattice Delaunay polytopes
Abstract
A perfect prismatoid is a convex polytope P such that for every its facet F the set vert(P) vert(F) belongs to a supporting hyperplane α F. We prove that every perfect prismatoid is affinely equivalent to some 0/1-polytope of the same dimension. (And therefore every perfect prismatoid is a lattice polytope.) Moreover, we prove that every perfect prismatoid is a lattice Delaunay polytope.
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