Allowed regions of galaxy-like (left column) and cluster-like (right column) polytropes in the relativistic regime. Dependence of the polytrope extension R and mass M on the parameters σ and ρ_c. For the polytropic indexes n = 3.5,  4.0,  4.5 (from top to bottom) we highlight the regions of later interest with a letter and number (the letter A is used for the galaxy-like polytropes, while the letter B is used for the cluster-like polytropes). Furthermore, the function ρ_crit is shown, where the shaded area is the area of nonexistent configurations for particular n.