DanA> Is there a proof that a 4-dimensional cube and 4-dimensional ball (sphere + interior) of the same volume are not scissors congruent? <DanAsimov I missed something. Is there a proof that a TWO-dimensional "cube" and TWO-dimensional "ball" (disk) of the same area are not interdissectible w/o A/C? It seems to me there's a lot of middle ground between "piece-wise smooth" (if that is indeed what scissors require) and "non-measurable". Also, I need to be educated as to how the following two conditions can be inequivalent: WDS> However, Dehn showed in one of the first Hilbert problem solves, that a regular tetrahedron and cube (same volume) are NOT scissors congruent. ----- DanA>I thought Dehn proved only that they could not each be dissected into the same finite set of polyhedra (up to isometries), analogous to the Bolyai dissections. ----- --rwg