Polarization singularities arising from the interference of three plane monochromatic waves with close propagation directions in a vacuum or a linear isotropic medium are studied within the framework of the quasi-optical approximation. With a special choice of linear polarization of waves, the conditions for the formation of L-lines in the cross section, where the polarization is linear, and C-points, where the polarization is circular, are determined, and analytical expressions are obtained for the location of such polarization singularities.