We study polynomials with complex coefficients which are nondegenerate with
respect to their Newton polyhedron through data on contact loci, motivic nearby
cycles and motivic Milnor fiber. Introducing an explicit description of these
quantities we can answer in part to questions concerning the motivic Milnor
fiber of the restriction of a singularity to a hyperplane and the integral
identity conjecture in the context of nondegenerate singularities. Moreover, in
the same context, we give calculations on the Hodge spectrum, the cohomology
groups of the contact loci as well as their compatibility with natural
automorphisms.