Multi-Twist Möbius Bands
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]