On the configurations of points in P2P2 with the Waldschmidt constant equal to two

Let Z={p1,…,pn}Z={p1,…,pn} be a configuration of points in the projective plane and let I=I(Z)I=I(Z) be its corresponding homogeneous ideal in K[P2]K[P2]. In this note, a geometric classification of all configurations of points in P2P2, for which the Waldschmidt constant of their defining ideals is equal to two, is given.