Main Question or Discussion Point
I would welcome the parametric equations for an embedding in R3 of a locally Euclidean Möbius Strip without self intersections nor singularities and of Gaussian curvature equal to zero. That it exists in R3 is trivial to prove: just get a strip of paper of appropriate length and width, twist and paste and you are done. Paper cannot be stretched so the intrinsic curvature of the animal is zero. You may perhaps appreciate looking at the ondulation of the Möbius Band while embedding in ordinary space. That one is the one I want to capture.