  We study oriented connected closed polyhedral surfaces with non-degenerate
triangular faces in three-dimensional Euclidean space, calling them polyhedra
for short. A polyhedron is called flexible if its spatial shape can be changed
continuously by changing its dihedral angles only. We prove that the polyhedron
is not flexible if for each of its edges the following holds true: the length
of this edge is not a linear combination with rational coefficients of the
lengths of the remaining edges. We prove also that if a polyhedron is flexible,
then some linear combinations of its dihedral angles remain constant during the
flex. In this case, the coefficients of such a linear combination do not alter
during the flex, are integers, and do not equal to zero simultaneously.
