Have you ever tried to create a mobius strip in Blender?
I would think the number one problem (if using a "one" sided mesh) will be to get past the normals...
me1958424 I had that problem too. It goes away if I solidify it.
nekronavt How did you do that? I tried using a curve, but I couldn't figure out how to give it a twist, so I ended up using a mesh instead.
williamatics I just created a bezier circle with a break in one point. One side of a break remains as it is and the second one has tilt of 180 deg. After that I convert it to the mesh and removed doubles.