Flow polytopes and the graph of reflexive polytopes

We suggest defining the structure of an unoriented graph R d on the set of reflexive polytopes of a fixed dimension d . The edges are induced by easy mutations of the polytopes to create the possibility of walks along connected components inside this graph. For this, we consider two types of mutations: Those provided by performing duality via nef-partitions, and those arising from varying the lattice. Then for d ≤ 3 , we identify the flow polytopes among the reflexive polytopes of each single component of the graph R d . For this, we present for any dimension d ≥ 2 an explicit finite list of quivers giving all d -dimensional reflexive flow polytopes up to lattice isomorphism. We deduce as an application that any such polytope has at most 6 ( d − 1 ) facets.