Any smooth asone hypersurface Z of complex dimension n deformation retracts to a cell complex of real dimension n. Starting from the Newton polytope of the defining function of Z, I will give an explicit combinatorial construction of a compact space S, comprised of n-dimensional components, which embeds into Z as a deformation retract. In particular, Z is homotopy equivalent to S. If time allows, I will discuss the relation of this work to the homological mirror symmetry program. This work is joint with Helge Ruddat, Nicollo Sibilla, and David Treumann.