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The following two-lobed blob is the union of two spheres, and it appears (?) that I can Export[] it to STL for 3d printing:

blob = Graphics3D[{Sphere[{0,0,0}, 1], Sphere[ {0,0,0.5}, 1]}]

How would I create the intersection instead of the union?

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You could try using geometric regions:

DiscretizeRegion[
 RegionIntersection[Ball[{0, 0, 0}, 1], Ball[{0, 0, 0.5}, 1]],
 MaxCellMeasure -> 0.0001
];

Export["blob.stl", %];
Import["blob.stl"]

reimported region

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