THE WEAKLY NEIGHBORLY POLYHEDRAL MAPS
Ulrich Brehm, Amos Altshuler · 1985
A weakly neighborly polyhedral map (w.n.p. map) is a 2-dimensional cell- complex which decomposes a closed 2-manifold without a boundary, such that for every two vertices there is a 2-cell containing them. We prove that there are just five distinct w.n.p, maps on the torus, and that only three of them are geometrically realizable as polyhedra with convex faces.