Non-degenerate polynomials and toric blow-ups

We will discuss the relationship between non-degenerate polynomials, Newton polyhedra (A.G. Kushnirenko, A.G. Khovanskii, A.N. Varchenko), and toric blow-ups. This relationship can be applied to a description of purely log terminal and canonical blow-ups of three-dimensional terminal toric singularities (see preprint http://arxiv.org/abs/1501.00129).