An enumeration of combinatorial 3-manifolds with nine vertices

A. Altshuler; L. Steinberg

doi:10.1016/0012-365X(76)90138-2

An enumeration of combinatorial 3-manifolds with nine vertices

A. Altshuler, L. Steinberg

Department of Mathematics

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30 Scopus citations

Abstract

A complete classification is given for non-neighborly combinatorial 3-manifolds with nine vertices. It is found that there are 1246 such types, and that they all are spheres. It is shown that 1057 of those spheres are polytopal. i.e. can be realized as boundary complexes of convex 4-polytopes. 115 spheres are non-polytopal, and 74 spheres remain undecided.

Original language	English
Pages (from-to)	91-108
Number of pages	18
Journal	Discrete Mathematics
Volume	16
Issue number	2
DOIs	https://doi.org/10.1016/0012-365X(76)90138-2
State	Published - 1 Jan 1976

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(76)90138-2

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title = "An enumeration of combinatorial 3-manifolds with nine vertices",

abstract = "A complete classification is given for non-neighborly combinatorial 3-manifolds with nine vertices. It is found that there are 1246 such types, and that they all are spheres. It is shown that 1057 of those spheres are polytopal. i.e. can be realized as boundary complexes of convex 4-polytopes. 115 spheres are non-polytopal, and 74 spheres remain undecided.",

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AB - A complete classification is given for non-neighborly combinatorial 3-manifolds with nine vertices. It is found that there are 1246 such types, and that they all are spheres. It is shown that 1057 of those spheres are polytopal. i.e. can be realized as boundary complexes of convex 4-polytopes. 115 spheres are non-polytopal, and 74 spheres remain undecided.

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An enumeration of combinatorial 3-manifolds with nine vertices

Abstract

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