Lattice characterization of convex 3-polytopes and of polygonizations of 2-manifolds

Amos Altshuler

doi:10.1007/BF02771551

Lattice characterization of convex 3-polytopes and of polygonizations of 2-manifolds

Amos Altshuler

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let C be a polygonization of a 2-dimensional closed manifold without boundary, and L(C) the set of all the faces of C, partially ordered by inclusion, with adjoinment of a minimal and a maximal element. Then L(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.

Original language	English
Pages (from-to)	57-64
Number of pages	8
Journal	Israel Journal of Mathematics
Volume	8
Issue number	1
DOIs	https://doi.org/10.1007/BF02771551
State	Published - 1 Mar 1970
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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title = "Lattice characterization of convex 3-polytopes and of polygonizations of 2-manifolds",

abstract = "Let C be a polygonization of a 2-dimensional closed manifold without boundary, and L(C) the set of all the faces of C, partially ordered by inclusion, with adjoinment of a minimal and a maximal element. Then L(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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AB - Let C be a polygonization of a 2-dimensional closed manifold without boundary, and L(C) the set of all the faces of C, partially ordered by inclusion, with adjoinment of a minimal and a maximal element. Then L(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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Lattice characterization of convex 3-polytopes and of polygonizations of 2-manifolds

Abstract

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