Abstract
In previous papers, the author has shown that the polyhedral structures of fullerene type are widespread in the living and mineral worlds. They are most clearly manifested in the capsids of icosahedral viruses, the geometry of which has been well studied. This article demonstrates that the nomenclature, classification, and potential transformations of these polyhedral structures can be succinctly described by means of matrix algebra.
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REFERENCES
Caspar, D.L.D. and Klug, A., Physical principles in the construction of regular viruses, Cold Spring Harbor Symp. Quant. Biol., 1962, vol. 27, pp. 1–24.
Luria, S.E., Darnell, J.E., Jr., Baltimore, D., and Campell, A., General Virology, New York: John Wiley & Sons, 3rd ed., 1978.
Luria, S.E., Darnell, J.E., Jr., Baltimore, D., and Campell, A., Obshchaya virusologiya (General Virology), Moscow: Mir, 1981.
Rees, A.R. and Sternberg, M.J.E., From Cells to Atoms: an Illustrated Introduction to Molecular Biology, Oxford: Blackwell Sci. Publ., 1984.
Rees, A.R. and Sternberg, M.J.E., Vvedenie v molekulyarnuyu biologiyu: ot kletok k atomam (From Cells to Atoms: an Illustrated Introduction to Molecular Biology), Moscow: Mir, 2002.
Schmalz, T.G., Seitz, W.A., Klein, D.J., and Hite, G.E., Elemental carbon cages, J. Am. Chem. Soc., 1988, vol. 110, no. 4, pp. 1113–1127.
Voytekhovsky, Yu.L., Biomineral analogues in ontogeny and phylogeny, Paleontol. J., 2015, vol. 49, no. 14, pp. 1691–1697.
Voytekhovsky, Yu.L., Homological series of icosahedral viruses and fullerenes, Paleontol. J., 2016, vol. 50, no. 13, pp. 1505–1509.
Voytekhovsky, Yu.L. and Stepenshchikov, D.G., Fullerene transformations as analogues of radiolarian skeleton microevolution, Paleontol. J., 2016, vol. 50, no. 13, pp. 1544–1548.
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Translated by L. Lukyanov
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Voytekhovsky, Y.L. Algebraic Geometry of Icosahedral Viruses. Paleontol. J. 52, 1697–1700 (2018). https://doi.org/10.1134/S0031030118140216
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DOI: https://doi.org/10.1134/S0031030118140216