Abstract: Chow stability is one notion of Mumford's Geometric Invariant Theory for studying the moduli space of polarized varieties. Gelfand, Kapranov and Zelevinsky detected that Chow stability of polarized toric varieties is completely determined by its inherent `secondary polytope', which is a polytope whose vertices correspond to regular triangulations of the associated (Delzant) polytope. In this talk, we would like to discuss combinatorial framework for the Chow form of a (not-necessaliry-smooth) projective toric variety and its applications.