We derive the expression for the anisotropic heterogeneous matrices of permittivity and permeability associated with two-dimensional polygonal and star shaped cloaks. We numerically show using finite elements that the forward scattering worsens when we increase the number of sides in the latter cloaks, whereas it improves for the former ones. This antagonistic behavior is discussed using a rigorous asymptotic approach. We use a symmetry group theoretical approach to derive the cloaks design.