  We show that the F-theory dual of the heterotic string with unbroken
Spin(32)/Z_2 symmetry in eight dimensions can be described in terms of the same
polyhedron that can also encode unbroken E_8\times E_8 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.
