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I am trying to obtain 3D printable files from 3D plots with the code:

    modela = Plot3D[Sin[(x*y) + y^2], {x, -3, 3}, {y, -2, 2}, PlotTheme -> "ThickSurface", Axes -> False, Boxed -> False]

    Printout3D[modela, "modela.stl"]

My final .stl file appeared monochromatic. I do not know if I can really obtain .stl files with all colour details from the 3D plot preserved. Thank you in anticipation of your expert opinions and suggestions.

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As far as I'm aware, the STL format does not include any sort of lighting or coloring. I think that such files are simply lists of vertices of triangles and their associated normal vectors, which is all you need to construct a shape.

The printer itself and its associated material is where the color will come from; I don't personally know anything about that process. However, a quick google suggests that the VRML filetype can support color, and this filetype is supported by Mathematica (use .wrl as the file extension). Hopefully this will do what you're looking for!

Also, a quick tip: you can use the PlotPoints option to really smooth this out before printing. PlotPoints->120 seems to produce a very pleasant surface.

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