F-THEORY, SO(32) AND TORIC GEOMETRY

We show that the F-theory dual of the heterotic string with unbroken S pin(32)/Z(2) symmetry in eight dimensions can be described in terms of the same polyhedron that can also encode unbroken E-8 x E-8 symmetry. By considering particular compactifications with this K3 surface as a fiber, we can reproduce the recently found 'record gauge group' in si x dimensions and obtain a new 'record gauge group' in four dimensions. Our observations relate to the toric diagram for the intersection of components of degenerate fibers and our definition of these objects, w hich we call 'tops', is more general than an earlier definition by Can delas and Font. (C) 1997 Published by Elsevier Science B.V.