  A conjecture of Fuglede states that a bounded measurable set D, of measure 1,
can tile space by translations if and only if the Hilbert space L^2(D) has an
orthonormal basis consisting of exponentials exp(i 2 pi lambda x). If D has the
latter property it is called spectral. Let D be a polytope with the following
property: there is a direction u such that, of all the polytope faces
perpendicular to u, the total area of the faces pointing in the positive u
direction is more than the total area of the faces pointing in the negative u
direction. It is almost obvious that such a polytope D cannot tile space by
translation. We prove in this paper that such a domain is also not spectral,
which agrees with Fuglede's conjecture.
