2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60996For each strongly connected finite-dimensional (pure) simplicial complex we construct a finite group, the group of projectivities of the complex, which is a combinatorial but not a topological invariant. This group is studied for combinatorial manifolds and, in particular, for polytopal simplicial spheres. The results are applied to a coloring problem for simplicial (or, dually, simple) polytopes which arises in the area of toric algebraic varieties.16 pages, Latex2eCombinatoricsAlgebraic GeometryMetric Geometry52B05 (52B11; 52B70; 57Q15; 05C15; 14M25)text