Calculating Topological Indexes of Networks from the Corresponding Wells Point Symbol

Science Direct Working Paper No S1574-0331(04)70211-8

40 Pages Posted: 23 May 2017 Last revised: 9 Dec 2017

See all articles by Michael J. Bucknum

Michael J. Bucknum

Georgia College & State University - Department of Chemistry and Physics; Cornell University - Department of Chemistry and Chemical Biology

Date Written: February 2002

Abstract

This paper begins with a review of the Euler relation for the convex polyhedra. The Schläfli relation is derived from this by introducing the secondary topological indexes of polygonality and connectivity. A topology map of the polyhedra and extended structures, in a Schläfli space, is illustrated and is discussed from the point of view of its organizational value for defining the topological relationship of structures from their Schläfli indexes. A comment is then made with respect to the definition of the various vertex connectivities in structures, from knowledge of the circuit number of the vertex. It is shown here that vertices containing polar connections have a reduced circuit number from that calculated according to the prescription p(p-1)/2. Next a review is made of the Wells point symbols and corresponding Schläfli indexes; first of the regular diamond and graphene nets; second of the semi-regular nets, including the Archimedean fullerene polyhedron and the Cooperite structure-type, and the Catalan fluorite and Waserite structure-types; and third of the irregular nets to include the Wellsean glitter and phenacite structure-types. The direct translation of the Wells point symbol to a weighted average polygonality, n, and a weighted average connectivity, p, is demonstrated in these examples.

Keywords: Physical Chemistry > Solid State Chemistry and Materials, physchem/0202006

Suggested Citation

Bucknum, Michael J., Calculating Topological Indexes of Networks from the Corresponding Wells Point Symbol (February 2002). Science Direct Working Paper No S1574-0331(04)70211-8, Available at SSRN: https://ssrn.com/abstract=2969194

Michael J. Bucknum (Contact Author)

Georgia College & State University - Department of Chemistry and Physics ( email )

CBX 82
Milledgeville, GA 31061
United States

Cornell University - Department of Chemistry and Chemical Biology ( email )

Ithaca, NY 14853
United States

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