The (5x5 determinant) tetrahedron volume(<edges^2>) formula Fred mentioned is at http://mathworld.wolfram.com/Tetrahedron.html. I futzed the 22 cubic terms down to V = sqrt(s23 ((s14 + s13) s24 - (s24 - s14 - s12) s34 - s14 (s23 + s14 - s13 - s12) - s12 s13) + (s34 - s24 - s13 + s12) (s13 s24 - s12 s34) - (s13 - s12) s14 (s34 - s24))/12 (Best? Mma radicand LeafCount = 64, vs FullSimplify's 75.) Isn't this the purview of optimizing compilers? Rich recently showed me an application for "addition-subtraction-multiplication chains". One could imagine exhaustively (tree?) searching for the shortest instruction sequence yielding the 22 terms. Or if we could find a good proximity metric, would Veit Elser's (http://en.wikipedia.org/wiki/Difference_map_algorithm) methods apply? --rwg (DISTINGUISHEDLY THINLY-DISGUISED)