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Chemical applications of topology and group theory. 26. The sextuple diamond-square-diamond rearrangement of the icosahedron through a cuboctahedron intermediate

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Abstract

The details of the symmetry factoring of the graphs corresponding to the icosahedron and the cuboctahedron are presented. Such symmetry factoring procedures use the sequence of two-foldC 2 and threefoldC 3 elementsC 2 xC 2 x CZ x C3 to give disconnected graphs having eigenvalue spectra similar to those of the original polyhedra but with components having only one and two vertices. In addition, the same symmetry factoring sequence is used to determine the eigenvalue spectrum of an intermediate in the sextuple diamond-square process for conversion of the icosahedron to the cuboctahedron.

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References

  1. R.B. King, Inorg. Chem. 30 (1991)4437.

    Google Scholar 

  2. W.N. Lipscomb, Science 153 (1966)373.

    Google Scholar 

  3. B.M. Gimarc, J. Math. Chem. 5 (1990)359.

    Google Scholar 

  4. J.L. Hoard and R.E. Hughes, in:The Chemistry of Boron and its Compounds, ed. E.K. Muetterties (Wiley, New York, 1967) pp. 25–154.

    Google Scholar 

  5. D. Emin, T. Aselage, C.L. Beckel, I.A. Howard and C. Wood (eds.),Boron-Rich Solids, American Institute of Physics Conference Proceedings 140 (American Institute of Physics, New York, 1986).

    Google Scholar 

  6. D. Levine and P.J. Steinhardt, Phys. Rev. Lett. 53 (1984)2477.

    Google Scholar 

  7. D. Levine and P.J. Steinhardt, Phys. Rev. B34 (1986)596.

    Google Scholar 

  8. M. Audier, C. Janot, M. de Boissieu and B. Dubost, Phil. Mag. B60 (1989)437.

    Google Scholar 

  9. R.B. King, Inorg. Chim. Acta 181 (1991)217.

    Google Scholar 

  10. R.B. King, Inorg. Chim. Acta 116 (1986)125.

    Google Scholar 

  11. R.B. King, Int. J. Quant. Chem. Quant. Chem. Symp. 20 (1986)227.

    Google Scholar 

  12. D.F. Rieck, R.A. Montag, T.S. McKechnie and L.F. Dahl, J. Am. Chem. Soc. 108 (1986)1330.

    Google Scholar 

  13. M.T. Pope,Heteropoly and Isopoly Oxometallates (Springer, Berlin, 1983).

    Google Scholar 

  14. B.J. McClelland, J. Chem. Soc. Faraday Trans. II 70 (1974)1453.

    Google Scholar 

  15. B.J. McClelland, Mol. Phys. 45 (1982)189.

    Google Scholar 

  16. B.J. McClelland, J. Chem. Soc. Faraday Trans. II 78 (1982)911.

    Google Scholar 

  17. R.B. King, Theor. Chim. Acta 44 (1977)223.

    Google Scholar 

  18. S.S. D'Amato, Mol. Phys. 37 (1979)1363.

    Google Scholar 

  19. S.S. D'Amato, Theor. Chim. Acta 53 (1979)319.

    Google Scholar 

  20. R.A. Davidson, Theor. Chim. Acta 58 (1981)193.

    Google Scholar 

  21. M. Shen, Int. J. Quant. Chem. 38/1990)551.

    Google Scholar 

  22. K. Ruedenberg, J. Chem. Phys. 22 (1954)1878.

    Google Scholar 

  23. H.H. Schmidtke, J. Chem. Phys. 45 (1966)3920.

    Google Scholar 

  24. I. Gutman and N. Trinajstić, Topics Curr. Chem. 42 (1973)49.

    Google Scholar 

  25. R.B. King, B. Dai and B.M. Gimarc, Inorg. Chim. Acta 167 (1990)213.

    Google Scholar 

  26. A.J. Stone, Polyhedron 3 (1984)1299.

    Google Scholar 

  27. D.M.P. Mingos and R.J. Johnston, Struct. Bonding 68 (1987)29.

    Google Scholar 

  28. R.B. King and D.H. Rouvray, J. Am. Chem. Soc. 99 (1977)7834

    Google Scholar 

  29. R.B. King, in:Chemical Applications of Topology and Graph Theory, ed. R.B. King (Elsevier, Amsterdam, 1983) pp. 99–123.

    Google Scholar 

  30. R.B. King, in:Molecular Structure and Energetics, Vol. 1, ed. J.F. Liebman and A. Greenberg (VCH Publishers, Deerfield, 1986) pp. 123–148.

    Google Scholar 

  31. R.B. King, J. Math. Chem. 1 (1987)249.

    Google Scholar 

  32. R.B. King, Inorg. Chem. 27 (1988)1941.

    Google Scholar 

  33. R.B. King, J. Math. Chem. 4 (1990)69.

    Google Scholar 

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Authors and Affiliations

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

    R. Bruce King

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  1. R. Bruce King
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Additional information

This paper is dedicated to Professor Frank Harary in recognition of his pioneering work in areas of graph theory closely related to chemical problems. For part 25 of this series, see ref. [1].

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Bruce King, R. Chemical applications of topology and group theory. 26. The sextuple diamond-square-diamond rearrangement of the icosahedron through a cuboctahedron intermediate. J Math Chem 12, 9–16 (1993). https://doi.org/10.1007/BF01164621

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