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Polyhedral Dynamics

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Graph Theoretical Approaches to Chemical Reactivity

Part of the book series: Understanding Chemical Reactivity ((UCRE,volume 9))

Abstract

The concept of a polyhedron is a useful way for describing diverse chemical structures. In such a context a polyhedron may be regarded as a set consisting of (zero-dimensional) points, namely its vertices; (one-dimensional) lines connecting some of the vertices, namely its edges; and (two-dimensional) surfaces formed by the edges, namely its faces. Polyhedra can appear in chemical structures as coordination polyhedra in which the vertices represent ligands surrounding a central atom which is often, but not always, a metal, and cluster polyhedra in which the vertices represent multivalent atoms and the edges represent bonding distances. Deltahedra , in which all faces are triangles, are a special type of polyhedra which appear often in chemical contexts. Chemically significant deltahedra are depicted in Figure 1. The topology of a polyhedron can be described by a graph, called the 1-skeleton of the polyhedron. The vertices and edges of the 1-skeleton correspond to the vertices and edges, respectively, of the underlying polyhedron.

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Authors and Affiliations

  1. Department of Chemistry, University of Georgia, Athens, Georgia, 30602, USA

    R. B. King

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Editors and Affiliations

  1. Higher Institute of Chemical Technology, Burgas, Bulgaria

    Danail Bonchev  & Ovanes Mekenyan  & 

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© 1994 Springer Science+Business Media Dordrecht

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King, R.B. (1994). Polyhedral Dynamics. In: Bonchev, D., Mekenyan, O. (eds) Graph Theoretical Approaches to Chemical Reactivity. Understanding Chemical Reactivity, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1202-4_4

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  • DOI: https://doi.org/10.1007/978-94-011-1202-4_4

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  • Print ISBN: 978-94-010-4526-1

  • Online ISBN: 978-94-011-1202-4

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