The nonreciprocity of frequencies of counter-propagating waves and polarization characteristics of a ring resonator formed by totally reflecting prisms are studied. This resonator is shown to be characterized by the formation of polarization-inhomogeneous waves whose ellipsometric parameters depend on transverse coordinates. This is caused, on the one hand, by the spatial distribution of anisotropy in stressed totally reflecting prisms and, on the other hand, by the disagreement between the radii of curvature of the radiation wavefront and the optical surfaces of prisms. Polarization-inhomogeneous elements produce additional polarization loss, but have no effect on the nonreciprocity of frequencies of counter-propagating waves of a ring resonator in the absence of magnetic field.