MATTER FROM TORIC GEOMETRY

We present an algorithm for obtaining the matter content of effective six-dimensional theories resulting from compactification of F-theory o n elliptic Calabi-Yau threefolds which are hypersurfaces in toric vari eties. The algorithm allows us to read off the matter content of the t heory from the polyhedron describing the Calabi-Yau manifold. This is based on the generalized Green-Schwarz anomaly cancellation condition. (C) 1998 Elsevier Science B.V.