[math-fun] Hilbert 3 in 8D

Hilbert's 3rd problem (solved by Dehn) asks for a proof that a regular tetrahedron cannot be dissected into a finite number of pieces that can be put together to form a cube of the same volume. I believe the problem is easier in even dimensions. I want to dissect a tetrahedron (not necessarily regular, in fact a right simplex or orthoscheme is my favorite) into a brick (not necessarily regular) in 2d dimensions, for d >= 2. Has anyone seen any work on such higher-dimensional dissections? Neil Sloane (njas@research.att.com)