We show that if a polyhedron in the three-dimensional affine space with triangular faces is flexible, i.e., can be continuously

deformed preserving the shape of its faces, then there is a cycle of edges whose lengths sum up to zero once suitably

weighted by 1 and -1. We do this via elementary combinatorial considerations, made possible by a well-known

compactification of the three-dimensional affine space as a quadric in the four-dimensional projective space. The

compactification is related to the Euclidean metric, and allows us to use a simple degeneration technique that reduces the

problem to its one-dimensional analogue, which is trivial to solve.

This is a joint work with Georg Grasegger, Jan Legerský, and Josef Schicho.