F-theory, SO(32) and toric geometry

We show that the F-theory dual of the heterotic string with unbroken Spin(32)/Z2 symmetry in eight dimensions can be described in terms of the same polyhedron that can also encode unbroken E8 × E8 symmetry. By considering particular compactifications with this K3 surface as a fiber, we can reproduce the recently found ‘record gauge group’ in six 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, which we call ‘tops’, is more general than an earlier definition by Candelas and Font.