Tsikh† Institute of Mathematics and Computer Science Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia Received 18.09.2015, received in revised form 18.10.2015, accepted 25.10.2015 Consider a general polynomial of degree n with variable coefficients. <...> It is known that the Newton polytope of its discriminant is combinatorially equivalent to an (n−1)-dimensional cube. <...> The knowledge of this structure is important in the study of a general algebraic function y = y(a) of roots of the polynomial (1) ( [1, 2]). 1. <...> As for the monomial 18a0a1a2a3, it corresponds to an interior integer point (1, 1, 1, 1) ∈ N(∆), and the theorem says nothing about it. <...> The facets g2 and gn−2 of the Newton polytope N(∆) of the reduced discriminant ∆ are (n−2)-prisms. vI = vi1,.,is written down as follows (0, . . . , i1 i To prove Theorem 2 we need two lemmas. <...> Let i′ lie between ip On the Structure of the Classical Discriminant Evgeny N. Mikhalkin, Avgust K.Tsikh On the Structure of the Classical Discriminant Lemma 2. <...> Also, it is clear that the other this section is the following statement about discriminants of polynomials of degree not greater than 6. gk consisting of all monomials ∆ with exponents from gk. <...> The facet g4 is given by the system gk of its 2a3a4 −144a2 2a4+ 1a2a2 4+ 4 −144a2a2 3a3 4− Evgeny N. Mikhalkin, Avgust K.Tsikh On the Structure of the Classical Discriminant It is known that this discriminant is irreducible [4]. <...> Consider a general polynomial of degree n with variable coefficients. <...> It is known that the Newton polytope of its discriminant is combinatorially equivalent to an (n 1)-dimensional cube. <...> We show that two facets of this Newton polytope are prisms, and that truncations of the discriminant with respect to facets factor into discriminants of polynomials of smaller degree.! <...>