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RE: Why is it not possible to reassemble pieces of a broken solid?
About 1, wouldn't the jagged edges just connect to the other jagged edges, leading precipitously to yet more connections, until the parts were whole again? .. So I'm leaning toward 2, if those are the only options!
Well, again, if you manage to fit them precisely in the proper places on the microscopic level, than yes. Also I suspect that many jags would be bended or broken while cutting.
But again, I'm not sure. It's just my guess.
Today I learned (fact #4) that solid pieces really join together in space. See cold welding. So you must be right, the main problem is 2.
@irelandscape