Let's say, I have a closed 3D surface (say, the surface of a pebble). I want to pack it with spheres, but starting with the largest possible sphere, then the next largest possible nonoverlapping sphere and so on until I reach a specified lower limit on sphere size. Is there a unique solution? Is this a known, solved problem? Is there an obvious algorithmic approach to do this? Please advice. I am not in applied math or computational geometry, but love to wet my feet in these fine fields.
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An analogous process to the one you describe is known as Apollonian sphere packing:


