2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102166Regular triangulations of products of lattice polytopes are constructed with the additional property that the dual graphs of the triangulations are bipartite. The (weighted) size difference of this bipartition is a lower bound for the number of real roots of certain sparse polynomial systems by recent results of Soprunova and Sottile [Adv. Math. 204(1):116-151, 2006]. Special attention is paid to the cube case.new title; several paragraphs reformulated; 23 pagesCombinatoricsAlgebraic Geometry52B20; 14M25text