A systematic study of parameter matrices (scattering, impedances and admittances) of symmetrical three-ports with isotropic and gyrotropic media is carried out. A new classification of the three-ports based on geometrical symmetry with regard to the time reversal operator is suggested. The approach uses the theory of magnetic point groups, the Curie principle and the concept of gyrotropic symmetry and gyrotropic antisymmetry. All the possible parameter matrices of the three-ports with one-mode waveguides are obtained. The correspondence of these matrices to magnetic point groups of symmetry is determined.