Geodesic
Newton polyhedra and an algorithm for computing Hodge--Deligne numbers
Izvestiya. Mathematics , Tome 29 (1987) no. 2, pp. 279-298.

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An algorithm is given for computing the mixed Hodge structure (more precisely, the Hodge–Deligne numbers) for cohomology of complete intersections in toric varieties in terms of Newton polyhedra specifying the complete intersection. In some particular cases the algorithm leads to explicit formulas. Bibliography: 8 titles. 
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V. I. Danilov; A. G. Khovanskii. Newton polyhedra and an algorithm for computing Hodge--Deligne numbers. Izvestiya. Mathematics , Tome 29 (1987) no. 2, pp. 279-298. http://geodesic.mathdoc.fr/item/IM2_1987_29_2_a1/

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[6] Khovanskii A. G., “Mnogogranniki Nyutona i toricheskie mnogoobraziya”, Funkts. analiz i ego prilozh., 11:4 (1977), 56–67 | MR

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[8] Kempf G., Knudsen F., Mumford D., Saint-Donat B., Toroidal Embeddings. I, Lecture Notes in Mathematics, 339, Springer-Verlag, Berlin, 1973 | MR | Zbl