Christian Haase, Ilarion V. Melnikov
Abstract
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The reflexive dimension refldim(P) of a lattice polytope P is the minimal d so that P is the face of some d-dimensional reflexive polytope. We show that refldim(P) is finite for every P, and give bounds for refldim(kP) in terms of refldim(P) and k.
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The reflexive dimension refldim(P) of a lattice polytope P is the minimal d so that P is the face of some d-dimensional reflexive polytope. We show that refldim(P) is finite for every P, and give bounds for refldim(kP) in terms of refldim(P) and k.
Key concepts: Polytope, Birkhoff polytope, Combinatorics, Reflexivity, Lattice (music), Mathematics, Uniform k 21 polytope, Dimension (graph theory)