Isoperimetric Quotient for Fullerenes and Other Polyhedral Cages

The notion of Isoperimetric Quotient (IQ) of a polyhedron has been already introduced by Polya. It is a measure that tells us how spherical is a given polyhedron. If we are given a polyhedral graph it can be drawn in a variety of ways in 3D space. As the coordinates of vertices belonging to the same...

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Bibliographic Details
Published in:Journal of Chemical Information and Computer Sciences 1997-11, Vol.37 (6), p.1028-1032
Main Authors: Pisanski, Tomaž, Kaufman, Matjaž, Bokal, Drago, Kirby, Edward C, Graovac, Ante
Format: Article
Language:English
Subjects:
Chemical structures
Computerized information storage and retrieval
Fullerenes
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Summary:The notion of Isoperimetric Quotient (IQ) of a polyhedron has been already introduced by Polya. It is a measure that tells us how spherical is a given polyhedron. If we are given a polyhedral graph it can be drawn in a variety of ways in 3D space. As the coordinates of vertices belonging to the same face may not be coplanar the usual definition of IQ fails. Therefore, a method based on a proper triangulation (obtained from omni-capping) is developed that enables one to extend the definition of IQ and compute it for any 3D drawing. The IQs of fullerenes and other polyhedral cages are computed and compared for their NiceGraph and standard Laplacian 3D drawings. It is shown that the drawings with the maximal IQ values reproduce well the molecular mechanics geometries in the case of fullerenes and exact geometries for Platonic and Archimedean polyhedra.
ISSN:0095-2338
1549-960X
DOI:10.1021/ci970228e