How is the thickness defined in ParametricPlot3D? For 2D plots, the thickness "is given as a fraction of the horizontal plot range," but how does that work in 3D for the following example? Also, it doesn't seem that AbsoluteThickness works.
Moebius[R, a, b_] := {(R + a Cos[b/2]) Cos[b], (R + a Cos[b/2]) Sin[b], a Sin[b/2]}
MBand = ParametricPlot3D[Moebius[5, a, b], {a, -1, 1}, {b, 0, 2 Pi}, Mesh -> None, PlotPoints -> {20, 100}, MaxRecursion -> 0, PlotRange -> All, PlotStyle -> Directive[{Thickness[1], Opacity[0.5]}]]
