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Huh. So mathematically, I guess a bowling ball is a pair of pants.

I think a bowling ball would actually just be a solid topologically. The finger holes are just indentations rather than holes that go all the way through. IANAT, though.

Ok correct, technically I guess the outer 2D surface of a bowling ball is a pair of pants. For the entire 3D object to qualify, the holes would have to be connected internally.

Depends on how many many holes are in the jeans.