Einfache, konvexe Polytope und ihre Graphen
type: Item
instance of: scholarly article
title: Einfache, konvexe Polytope und ihre Graphen
zbMATH Open document ID: 0565.52004
author: Wolfgang Schöne
published in: Beiträge zur Algebra und Geometrie
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/138299
review text: A d-polytope is the convex hull of a finite number of affinely independent points in d-dimensional space. The faces of a d-polytope are the intersections of the d-polytope with a supporting hyperplane. A k- face is a k-dimensional face. The set of k-faces \((k=-1,...,d)\) of each d-polytope form a combinatorial complex. Two d-polytopes are combinatorially equivalent if their associated combinatorial face- complexes are isomorphic. The graph of a d-polytope is the graph formed by its 0-faces (vertices) and 1-faces (edges). It is well known that two 3-polytopes with isomorphic graphs are combinatorially equivalent. This property does not, however, generalize to higher dimensions. A d-polytope is simple if each of its vertices is contained in exactly d different d-1 faces. Its graph is then always regular of degree d. In this paper it is shown that two simple 4-polytopes with isomorphic graphs are always combinatorially equivalent.
reviewed by: Frank Plastria
Mathematics Subject Classification ID: 52Bxx
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 57M15
zbMATH DE Number: 3901547
zbMATH Keywords: combinatorially equivalent
zbMATH Keywords: graph of a d-polytope
zbMATH Keywords: simple 4-polytopes
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3901547