How to struggle with the beauty and symmetry of soccer ball fullerene–personal history

Document Type : Original Article


Ochanomizu University (Emeritus), Bunkyo-ku, Tokyo 112-8610, Japan


On this occasion I thought that it is meaningful to trace back and document my personal history involved in this beautiful soccer ball shape and molecule C60 not only for myself but also for the next generation to follow. Therefore, the topics may be moving to and fro in the 4-dimensional world. If the readers find any inaccurate description, please, remind its corrections
or additions to me privately or to the public freely.

Graphical Abstract

How to struggle with the beauty and symmetry of soccer ball fullerene–personal history

[1] J. Aihara, A new definition of Dewar-type resonance energies, J. Am. Chem. Soc. 98 (1976) 2750–2758.
[2] J. Aihara, H. Hosoya, Spherical aromaticity of buckminsterfullerene, Bull. Chem. Soc. Jpn. 61 (1988) 2657–2659.
[3] M. Arezoomand, On the distance-based topological indices of fullerenes and fullerenyl anions having dendrimer units, Digest J. Nanomaterials and Biostructures, 4 (4) (2009) 713–722.
[4] A. T. Balaban, Ed., From Chemical Topology to Three Dimensional Geometry, Kluwer Academic Publ., New York, 1999.
[5] A. T. Balaban, O. Ivanciuc, in Topological Indices and Related Descriptors in QSAR and QSPR, J. Devillers, A. T. Balaban (Eds.), Gordon and Breach, Amsterdam, (1999) 21–57.
[6] F. Cataldo, A. Graova´c, O. Ori, The Mathematics and Topology of Fullerenes, Springer, Heidelberg, 2011.
[7] R. A. Davidson, Spectral analysis of graphs by cyclic automorphism subgroups, Theor. Chim. Acta, 58 (1981) 193–231.
[8] P.W. Fowler, D. E. Manolopoulos, An Atlas of Fullerenes, Clarendon Press, Oxford (1995).
[9] P.W. Fowler, Resistance distances in fullerene graphs, Croat. Chem. Acta, 75 (2002) 401–408.
[10] E. J. Farrell, An introduction to matching polynomials, J. Comb. Theory, B27 (1979) 75–86.
[11] I. Gutman, M. Milun, N. Trinajsti´c, Non-Parametric Resonance Energies of Arbitrary Conjugated Systems, J. Am. Chem. Soc. 99 (1977) 1692–1704.
[12] H. Hargittai (Ed.), Symmetry Unifying Human Understanding, Pergamon Press, New York, 1986.
[13] J. L. Hoard, R. E. Hughes, The Chemistry of Boron and Its Compounds, E. L. Mutterties (Ed.), John Wiley, N. Y. 1967.
[14] H. Hosoya, Topological index, a newly proposed quantity characterizing the topological nature of structure isomers of saturated hydrocarbons, Bull. Chem. Soc. Jpn. 44 (1971) 2332–2339.
[15] H. Hosoya, M. Murakami, M. Gotoh, Distance polynomial and characterization of a graph, Natl. Sci. Rept., 24, Ochanomizu Univ, (1973) 27–34.
[16] H. Hosoya, K. Hosoi, I. Gutman, A topological index for the total p-electron energy. Proof of a generalised Huckel rule for an arbitrary network, Theor. Chim. Acta, 38 (1975) 37–47 (Berlin).
[17] H. Hosoya, T. Yamaguchi, Sextet polynomial. A new enumeration and proof technique for the resonance theory applied to the aromatic hydrocarbons, Tetrahedron Lett. (1975) 4659–4662.
[18] H. Hosoya, Gendai Kagaku (Chemistry Today), 102 (9) (1979) 38–45 (in Nihongo).
[19] H. Hosoya, Gendai Kagaku (Chemistry Today), 103 (10) (1979) 34–42 (in Nihongo).
[20] H. Hosoya, Gendai Kagaku (Chemistry Today), 105 (12) (1979) 40–47 (in Nihongo).
[21] H. Hosoya, Newton, 2 (1982) (5), 36-43 (in Nihongo).
[22] H. Hosoya, Kagaku wo Tsukamu (To Grasp Chemistry), Iwanami, Tokyo (1983) (in Nihongo).
[23] H. Hosoya, Matching and symmetry of graphs, Comp. Math. Appl. 12B (1986) 271–290.
[24] H. Hosoya, Gendai Kagaku (Chemistry Today), 201 (12) (1987) 38–44 (in Nihongo).
[25] H. Hosoya, On some counting polynomials in chemistry, Discr. Appl. Math., 19 (1988) 239–257.
[26] H. Hosoya, Y. Tsukano, Efficient Way for Factorization the Characteristic Polynomial of Highly Symmetrical Graphs Such as the Buckminsterfullerene, Fullerene Sci. Tech., 2 (1994) 381–393.
[27] H. Hosoya, Y. Maruyama, Efficient generation of the cartesian coordinates of truncated icosahedron and related polyhedra, J. Mol. Graphics Modelling, 19 (2001) 205–209.
[28] H. Hosoya, Bull. Japan Soc. Phys. Chem. Education, 76 (2) (2005) 1–23 (in Nihongo).
[29] H. Hosoya, What can mathematical chemistry contribute to the development of mathematics? Int’l. J. Philosophy of Chem. (HYLE), 19 (2013) 87–105.
[30] S. Iwata, H. Hosoya, unpublished work. For all the coefficients see K. Balasubramanian, Chem.Phys. Lett. 239 (1995) 117–123.
[31] D. J. Klein, T. G. Schmalz, G. E. Heit, W. A. Seitz, Resonance in C60 buckminsterfullerene, J. Am.Chem. Soc. 108 (1986) 1301–1302.
[32] W. Kratchmer, L. D. Lamb, K. Fostiropoulos, D. R. Huffman, Solid C60: a new form of carbon, Nature, 347 (1990) 354–358.
[33] H.W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl, R. E. Smalley, C60: Buckminsterfullerene, Nature, 318 (1985) 162–163.
[34] H.W. Kroto, A. W. Alaff, S. P. Balm, C60 : Buckminsterfullerene, Chem. Rev. 91 (1991) 1213–1235.
[35] S. Nagakura, H. Hosoya, Structure and Properties, Tokyo Kagakudojin, Tokyo (1970) (in Nihongo).
[36] E. Osawa, Kagaku (Chemistry), 25 (1970) 854–863 (in Nihongo=Language used in Japan); Chem. Abstr. 74 (1971) 75698v.
[37] W.-C. Shiu, P. C. B. Lamb, H. Zhang, Clar and sextet polynomials of buckminsterfullerene, J. Mol. Struct. THEOCHEM), 622 (2003) 239–248.
[38] Z. Yoshida, E. Osawa, Aromaticity, Kagakudojin, Kyoto (1971), pp. 174–178 (in Nihongo).
Volume 7, Issue 1
January 2022
Pages 1-14
  • Receive Date: 11 February 2022
  • Revise Date: 17 February 2022
  • Accept Date: 01 March 2022
  • Publish Date: 10 March 2022