  A smooth affine hypersurface Z of complex dimension n is homotopy equivalent
to an n-dimensional cell complex. Given a defining polynomial f for Z as well
as a regular triangulation of its Newton polytope, we provide a purely
combinatorial construction of a compact topological space S as a union of
components of real dimension n, and prove that S embeds into Z as a deformation
retract. In particular, Z is homotopy equivalent to S.
