Abstract
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.
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Brehm, U., Altshuler, A. The weakly neighborly polyhedral maps on the torus. Geom Dedicata 18, 227–238 (1985). https://doi.org/10.1007/BF00181222
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DOI: https://doi.org/10.1007/BF00181222