Möbius strips with 1, 3, 5, and 7 twists. These .stl files were exported straight from Mathematica, and then run though Netfabb to repair a few defects in the mesh . Sometimes shapes like the Möbius can have problems with their normal orientation, but I think these are ok for printing. They check out as "orientable" in Netfabb's analysis anyway. I've printed them all without problems. Here is the Mathematica code I used, for those who are interested in such things... twists = 5; ( number of twists) width = 1.2; ( width of "ribbon" ) thickness = 1; ( thickness of "ribbon" ) Export["5twistmobius.stl", ParametricPlot3D[{(1 + v/2Cos[twists/2u])Cos[u], (1 + v/2Cos[twists/2u])Sin[u], v/2Sin[twistsu/2]}, {u, 0, 2*Pi}, {v, -width, width}, PlotStyle -> Thickness[thickness], PlotPoints -> 10, MaxRecursion -> 5]]; ParametricPlot3D[{(1 + v/2Cos[twists/2u]) Cos[u], (1 + v/2Cos[twists/2u])Sin[u], v/2Sin[twistsu/2]}, {u, 0, 2*Pi}, {v, -width, width}, PlotStyle -> Thickness[thickness], PlotPoints -> 20, MaxRecursion -> 10]