Newton-Okounkov bodies obtained from certain orbits of plabic graphs

Abstract: We investigate the plabic graphs corresponding to the quadrilateral Postnikov arrangements used by J.Scott to equip the homogeneous coordinate rings of Grassmannians with a cluster structure. More precisely we describe their orbits under the natural action of the dihedral group and show that the associated Newton-Okounkov bodies are all unimodular equivalent to Gelfand-Tsetlin polytopes.