  In this paper we study intersections of quadrics, components of the
hypersurface in Grassmannian $Gr(3, \CC^n)$ introduced in \cite{SoSuSi}. This
lead to an alternative statement and proof of Pappus's Theorem retrieving
Pappus's and Hesse configurations of lines as special points in complex
projective Grassmannian. This new connection is obtained through a third purely
combinatorial object, the intersection lattice of Discriminantal arrangement.
