We describe a practical and effective method for reconstructing the
deformation class of a Fano manifold X from a Laurent polynomial f that
corresponds to X under Mirror Symmetry. We explore connections to nef
partitions, the smoothing of singular toric varieties, and the construction of
embeddings of one (possibly-singular) toric variety in another. In particular,
we construct degenerations from Fano manifolds to singular toric varieties; in
the toric complete intersection case, these degenerations were constructed
previously by Doran--Harder. We use our method to find models of orbifold del
Pezzo surfaces as complete intersections and degeneracy loci, and to construct
a new four-dimensional Fano manifold.