A Stylized Klein Bottle

First, we define the necessary functions to describe the surface.

bx=6*Cos[u]*(1+Sin[u]);
by=16*Sin[u];
rad=4*(1-Cos[u]/2);
X=If[Inequality[Pi,Less,u,LessEqual,2*Pi],bx+rad*Cos[v+Pi],bx+rad*Cos[u]*Cos[v]];
Y=If[Inequality[Pi,Less,u,LessEqual,2*Pi],by,by+rad*Sin[u]*Cos[v]];
Z=rad*Sin[v];

Next, we define the opacity value to be used for the "holes".

o=.2;

Then, we define the colors to be used for the surface which alternates between transparent-blue, and gray.

col1=Blue;
col2=Gray;

We define 3 light sources.

darklights={{"Directional",RGBColor[0.5, 0.5, 1],ImageScaled[{0, 1, 0}]}, 
     {"Directional",RGBColor[1, 0.5, 0.5],ImageScaled[{1, -1, 0}]}, {"Directional",RGBColor[0.5, 1, 0.5],ImageScaled[{-1, -1, 0}]}};

Now we create the graphic.

gr=ParametricPlot3D[{X,Y,Z},{u,0,2*Pi},{v,0,2*Pi},PlotPoints->{48,12},Axes->False,Boxed->False,Mesh->59,MeshShading->{{{col1,Opacity[o],Specularity[White,128]},{col1,Opacity[o],Specularity[White,128]},{col2,Specularity[White,128]}},{{col1,Opacity[o],Specularity[White,128]},{col1,Opacity[o],Specularity[White,128]},{col2,Specularity[White,128]}},{{col1,Opacity[o],Specularity[White,128]},{col1,Opacity[o],Specularity[White,128]},{col2,Specularity[White,128]}},{{col2,Specularity[White,128]},{col2,Specularity[White,128]},{col2,Specularity[White,128]}}},MeshStyle->GrayLevel[.3],ImageSize->{1280,1024},MeshFunctions->{#4&,#5&},Background->Black,Lighting->darklights,SphericalRegion->True,ViewAngle->π/12]

Export["C:\\Documents and Settings\\jeffb\\Desktop\\klein60-1280x1024.png",gr]