Graphs of polyhedra; polyhedra as graphs
type: Item
instance of: scholarly article
title: Graphs of polyhedra; polyhedra as graphs
zbMATH Open document ID: 1111.51018
author: Branko Grünbaum
published in: Discrete Mathematics
publication date: 2007-02-13T00:00:00Z
full work available at URL: http://hdl.handle.net/1773/2276
review text: The article studies relationships between graphs and polyhedra in two contexts. In the first, Steinitz's Theorem about convex polyhedra is revisited and the one-to-one correspondence between convex polyhedra and 3-connected planar graphs is described in detail. In the second, graphs are employed to define and study abstract and geometric polyhedra, with the goal to provide a rigorous approach to the theory of nonconvex polyhedra. Included are detailed comments about the history of the theory of polyhedra.
reviewed by: Egon Schulte
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 52B10
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 5124963
zbMATH Keywords: polygon
zbMATH Keywords: 3-connected planar graphs
zbMATH Keywords: Steinitz's Theorem
zbMATH Keywords: convex polyhedron
zbMATH Keywords: nonconvex polyhedron
zbMATH Keywords: abstract polyhedron
MaRDI profile type: Publication
OpenAlex ID: W1979306170
Wikidata QID: Q56047069
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DOI: 10.1016/J.DISC.2005.09.037
DBLP publication ID: journals/dm/Grunbaum07
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description: scientific article; zbMATH DE number 5124963