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Applying transformations to data coming from an STL file

I am very new with the use of 3D graphics in Mathematica, so my question might be very naive. I need to Import an STL file, apply transformations to it (rotation and translation), and export it back ...
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Geometric Transformation not working - degenerate points?

I've successfully used FindGeometricTransformation to project the simplex triangle onto the x-y plane: ...