For a graph G, let be the probability that three distinct random vertices span exactly i edges. We call the 3-local profile of G. We investigate the set of all vectors that are arbitrarily close to the 3-local profiles of arbitrarily large graphs. We give a full description of the projection of to the plane. The upper envelope of this planar domain is obtained from cliques on a fraction of the vertex set and complements of such graphs. The lower envelope is Goodman's inequality . We also give a full description of the triangle-free case, i.e. the intersection of with the hyperplane . This planar domain is characterized by an SDP constraint that is derived from Razborov's flag algebra theory.