I'm looking for the correct name of geometric structures obtained as follows. 2-structures: A collection $X$ of triangles is a $2$-structure. If $X$ is a $2$-structure and $Y$ is obtained from $X$ by gluing two free edges belonging to triangles in $X$, then $Y$ is a $2$-structure. 3-structures: A collection $X$ of tetrahedra is a $3$-structure. If $X$ is a $3$-structure and $Y$ is obtained from $X$ by gluing two free triangles belonging to tetrahedra in $X$, then $Y$ is a $3$-structure. k-structures: A collection $X$ of $k$-simplices is a $k$-structure. If $X$ is a $k$-structure and $Y$ is obtained from $X$ by gluing two free (k-1)-simplices belonging to $k$-simplices in $X$, then $Y$ is a $(k-1)$-structure. Alternatively, a $k$-structure can be non-inductively defined as a homogeneous simplicial k-complex $X$, satisfying the following conditions.The intersection of any two k-simplices in X is either empty or a (k-1) simplex. Each (k-1)-simplex is the intersection of at most two $k$-simplices in $X$.Question: What is the correct name for $k$-structures? 
Structures obtained by gluing simplices
reference request;computational geometry;topology;topological graph theory;simplicial complexes