Re: [math-fun] tetrahedron volume

On 10/20/08, Fred lunnon <fred.lunnon@gmail.com> wrote:

Of course, these do not represent tetrahedra; but it shouldn't be hard to concoct similar "proper" examples where all values involved are positive; also perhaps rational.

I didn't look very hard ... Taking U43 = 1, and U21 = 1, 3 in turn: the first tetrahedron is equilateral, the second flat, and both have all 16 x face areas^2 = 3. WFL Sufficient conditions for embeddability are that every possible D_k determinant is non-negative; or else that there is some increasing sequence of elements ("flag manifold") for which the D_k are all positive. WFL