A characterization of triangulations of closed surfaces

In this paper we prove that a finite triangulation of a connected closed surface is completely determined by its intersection matrix. The \emph{intersection matrix} of a finite triangulation, $K$, is defined as $M_K=(dim(s_i\cap s_j){)}_{0\le i,0\le j}^{n-1}$, where $K_{2}={s_{0}, \ldots s_{n-1}}$isalabellingofthetrianglesof$K$.