The reflexive dimension of a lattice polytope
  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. 
Christian Haase and Ilarion V. Melnikov