Journal
DISCRETE MATHEMATICS
Volume 307, Issue 3-5, Pages 445-463Publisher
ELSEVIER
DOI: 10.1016/j.disc.2005.09.037
Keywords
polygon; 3-connected planar graph; Steinitz's theorem; convex polyhedron; nonconvex polyhedron; abstract polyhedron
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Relations between graph theory and polyhedra are presented in two contexts. In the first, the symbiotic dependence between 3-connected planar graphs and convex polyhedra is described in detail. In the second, a theory of nonconvex polyhedra is based on a graph-theoretic foundation. This approach eliminates the vagueness and inconsistency that pervade much of the literature dealing with polyhedra more general than the convex ones. (c) 2006 Elsevier B.V. All rights reserved.
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