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Molecular modeling of fullerenes with hexastrips

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References and Notes

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  2. See, for example, Gerdes, P.Educational Studies in Mathematics 1988, 19, 137–162; Gerdes, P.Ethnogeometrie: Kulturanthropologische Beiträge zur Genese und Didaktik der Geometrie; Franzbecker Verlag: Bad Salzdethfurth, 1990; pp 282–287

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  3. For examples and references, see Gerdes, P.Ethnogeometrie: Kulturanthropologische Beiträge zur Genese und Didaktik der Geometrie; Franzbecker Verlag: Bad Salzdethfurth, 1990; pp 52–53. Further examples may be found in Faublée,J. Ethnographie de Madagascar, Musée de l’Homme: Paris, 1946; pp 19, 28, 38; Somjee, S.Material Culture of Kenya, East African Educational Publishers: Nairobi, 1993, 96; Meurant, G.; Thompson, R.F.Mbuti Design-Paintings by Pygmy Women of the Ituri Forest, Thames and Hudson: London, 1995, 162; Guss, D.M.To Weave and Sing-Art, Symbol, and Narrative in the South American rain Forest, University of California: Berkeley, 1989, 73; Lane, R.F.Philippine Basketry: an Appreciation, Bookmark Inc.: Manila, pp 14, 44, 152, 170, 213; Ranjan, M.P.,Bamboo and Cane crafts of North East India, National Institute of Design, 1986

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  4. Cf. Gerdes, P. InFivefold Symmetry; Hargittai, I., Ed.; World Scientific: Singapore, 1992; pp 245–261

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  7. Cf. e.g. Kroto, H.; Fischer, J.; Cox, D., Eds.,The Fullerenes, Pergamon Press: Oxford, 1993, pp 1, 11; Hirsch, A.The Chemistry of Fullerenes, George Thieme Verlag: Stuttgart, 1994, 5; Dresselhaus, M.S.; Dresselhaus, G.; Ecklund, P.C.Science of Fullerenes and Carbon Nanotubes, Academic Press, San Diego, 1996, 2

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  8. As can be see in a photograph in Snyder, R., Ed.Buckminster Fuller: Autobiographical Monologue/Scenario, St. Martin’s Press: New York, 1980, p 151

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  11. Cf., e.g., Fowler, P.W.; Austin, S.J.; Manolopoulos, D.E. InPhysics and Chemistry of the Fullerenes, Prassides, K., Ed.; Kluwer Academic Publishers: Dordrecht, 1994; pp 41–62

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  12. See [11] and Fowler, P.W.; Manolopoulos, D.E.; Ryan, R.P. InThe Fullerenes, Kroto, H.; Fischer, J.; Cox, D., Eds. Pergamon Press: Oxford, 1993, pp 97–112

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  13. Hexastrip weavable isomers are what Schmalz and Klein call Clar Sextet isomers, having in common a special sort of Kekulé structure possessed by no other fullerenes. In this structure every pentagon has five exo double bonds and every double bond is seen to take part in two conjugated 6-circuits, what represents the maximum possible stabilizing contribution from a Kekulé structure. Schmalz and Klein show that such Kekulé structures are only possible for buckminsterfullerene and fullerenes having 60 + 6m atoms for m>1. See Schmalz, T.G.; Klein, D.J. InBuckminsterfullerenes, Billups, W.E.; Ciufolini, M.A., Eds. VCH: New York, 1993, pp 83–101. The leapfrog fullerenes belong to the Clar Sextet isomers. Cf. Fowler, P.W.; Manolopoulos, D.E.; Ryan, R.P. InThe Fullerenes, Kroto, H; Fischer, J.; Cox, D., Eds. Pergamon Press: Oxford, 1993, pp 102–103

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  14. This cluster appears among the possible C24 clusters analyzed by Cioslowski, J.Electronic Structure Calculations on Fullerenes and Their Derivatives, Oxford University Press, New York, 1995, pp 162–164. Cf. also Terrones, H.; Mackay A.L. InThe Fullerenes, Kroto, H.; Fischer, J.; Cox, D., Eds. Pergamon Press: Oxford, 1993, p 115

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  1. Universidade Pedagógica, C.P. 915 Maputo, Mozambique

    Paulus Gerdes

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Reprinted with permission fromThe Chemical Intelligencer Vol. 4 (1).

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Gerdes, P. Molecular modeling of fullerenes with hexastrips. Math Intelligencer 21, 6–12 (1999). https://doi.org/10.1007/BF03024824

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