Triangulated n-manifolds are determined by their [n2] + 1-skeletons

We will reconstruct compact, triangulated n-manifolds—without-boundaries from just their $\text{n}\text{2}\text{] + 1}$ skeletons. Therefore, two such manifolds are isomorphic if they have simplicially isomorphic $\text{n}\text{2}\text{+ 1}$-skeletons. Furthermore, when n is even, and the $\text{n}\text{2}$-homology group is zero, then the $\text{n}\text{2}$-skeleton is sufficient.