Abstract
LetC be a polygonization of a 2-dimensional closed manifold without boundary, andL(C) the set of all the faces ofC, partially ordered by inclusion, with adjoinment of a minimal and a maximal element. ThenL(C) is a lattice, and its characterization is given here. Also a characterization of the lattice of the faces of a convex 3-polytope is given.
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References
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This is a part of the author’s Ph.D. dissertation, written under the supervision of Professor H. Furstenberg, and submitted to the Hebrew University in June, 1969.
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Altshuler, A. Lattice characterization of convex 3-polytopes and of polygonizations of 2-manifolds. Israel J. Math. 8, 57–64 (1970). https://doi.org/10.1007/BF02771551
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DOI: https://doi.org/10.1007/BF02771551