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We consider the following two families of lattice-free polytopes: the family $\\mathcal{L}^d$ of integral lattice-free polytopes in $\\mathbb{R}^d$ that are not properly contained in another integral lattice-free polytope and its subfamily $\\mathcal{M}^d$ consisting of integral lattice-free polytopes in $\\mathbb{R}^d$ which are not properly contained in another lattice-free set. 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We consider the following two families of lattice-free polytopes: the family $\\mathcal{L}^d$ of integral lattice-free polytopes in $\\mathbb{R}^d$ that are not properly contained in another integral lattice-free polytope and its subfamily $\\mathcal{M}^d$ consisting of integral lattice-free polytopes in $\\mathbb{R}^d$ which are not properly contained in another lattice-free set. 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