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It seems to me the "sphere packing" infill would be subject to the sagging-overhang issues that arise on additive-extrusion devices. And of course, the infill is not a place where you would have your slicer add support material...

Maybe I'm just not picturing the arrangement of the infill geometry correctly... The dodecahedron infill seems interesting, though....

If done fast and at the right temp, you can manage up to 10mm flat bridges with very little sagging.
Well most spheres actually print nicely at that size (radius being less than 10mm or so), but yes, sagging can occur. That was just the first test infill, it didn't really hold any significant value or anything. The other infills are much better. (Author of the software btw)
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Is this meant to be used as a replacement for the infill created by the Slicer?
Yes. Those infills are usually just a 2d image which is drawn in the hollo part of the model for each layer.
Very interesting idea - particularly the dynamic struct to vertext