  We present an algorithm for obtaining the matter content of effective
six-dimensional theories resulting from compactification of F-theory on
elliptic Calabi-Yau threefolds which are hypersurfaces in toric varieties. The
algorithm allows us to read off the matter content of the theory from the
polyhedron describing the Calabi-Yau manifold. This is based on the generalized
Green-Schwarz anomaly cancellation condition.
