  The polarization of light can exhibit unusual features when singular optical
beams are involved. In 3-dimensional polarized random media the polarization
orientation around singularities describe 1/2 or 3/2 M\"obius strips. It has
been predicted that if singular beams intersect non-collinearly in free space,
the polarization ellipse rotates forming many-turn M\"obius strips or twisted
ribbons along closed loops around a central singularity. These polarization
features are important because polarization is an aspect of light that mediate
strong interactions with matter, with potential for new applications. We
examined the non-collinear superposition of two unfocused paraxial light beams
when one of them carried an optical vortex and the other one a uniform phase
front, both in orthogonal states of circular polarization. It is known that
these superpositions in 2-dimensions produce space-variant patterns of
polarization. Relying on the symmetry of the problem, we extracted the
3-dimensional patterns from projective measurements, and confirmed the
formation of many-turn M\"obius strips or twisted ribbons when the topological
charge of one of the component beams was odd or even, respectively. The
measurements agree well with the modelings and confirmed that these types of
patterns occur at macroscopic length scales and in ordinary superposition
situations.
