  Intersection homology is obtained from ordinary homology by imposing
conditions on how the embedded simplices meet the strata of a space $X$. In
this way, for the middle perversity, properties such as strong Lefschetz are
preserved. This paper defines local-global intersection homology groups, that
record global information about the singularities of $X$. They differ from
intersection homology in that stratified rather than ordinary simplices are
used. An example of such is $\sigma_j\times C\sigma_i$, where $\sigma_i$ and
$\sigma_j$ are ordinary simplices, and $C$ is the coning operator. The paper
concludes with a sketch of the relationship between local-global homology and
the geometry of convex polytopes. This paper is a more formal exposition of
part of the author's `Local-global intersection homology', alg-geom/9709011.
