We study the pattern of polarization that results in the crossing of two complex light beams with orthogonal circular polarizations. We recently showed experimentally that crossed beams in opposite circular polarization produce a twisting of the polarization in 3-dimensions. We did this with one beam in a mode bearing an optical vortex and the other in a Gaussian mode. In this work we extend to both beams bearing optical vortices. We find that Mobius strips appear when the difference in topological charge is odd, and twisted ribbons appear when the difference is even.