Abstract
We give a short solution of the kissing number problem in dimension three.
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References
Anstreicher, K.M.: The thirteen spheres: a new proof. Discret. Comput. Geom. 31(4), 613–625 (2004)
Böröczky, K.: The Newton–Gregory problem revisited. In: Discrete Geometry. Monogr. Textbooks Pure Appl. Math., vol. 253, pp. 103–110. Dekker, New York (2003)
Delsarte, P.: An Algebraic Approach to the Association Schemes of Coding Theory. Philips Res. Rep. Suppl., vol. 10. N.V. Philips’ Gloeilampenfabrieken, Eindhoven (1973)
Delsarte, P., Goethals, J.M., Seidel, J.J.: Spherical codes and designs. Geometriae Dedicata 6(3), 363–388 (1977)
Kabatyansky, G.A., Levenshtein, V.I.: Bounds for packings on the sphere and in space. Problemy Peredachi Informacii 14(1), 3–25 (1978). (in Russian)
Leech, J.: The problem of the thirteen spheres. Math. Gaz. 40, 22–23 (1956)
Levenshtein, V.I.: Boundaries for packings in \(n\)-dimensional Euclidean space. Dokl. Akad. Nauk SSSR 245(6), 1299–1303 (1979). (in Russian)
Maehara, H.: The problem of thirteen spheres—a proof for undergraduates. Eur. J. Comb. 28(6), 1770–1778 (2007)
Musin, O.R.: The kissing problem in three dimensions. Discret. Comput. Geom. 35(3), 375–384 (2006)
Musin, O.R.: The kissing number in four dimensions. Ann. Math. 168(1), 1–32 (2008)
Odlyzko, A.M., Sloane, N.J.A.: New bounds on the number of unit spheres that can touch a unit sphere in \(n\) dimensions. J. Comb. Theory Ser. A 26(2), 210–214 (1979)
Pfender, F.: Improved Delsarte bounds for spherical codes in small dimensions. J. Comb. Theory Ser. A 114(6), 1133–1147 (2007)
Schütte, K., van der Waerden, B.L.: Das Problem der dreizehn Kugeln. Math. Ann. 125, 325–334 (1953)
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The author thanks three anonymous referees whose help allowed him to fix the case of three points and improve the readability of the paper in general.
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Glazyrin, A. A Short Solution of the Kissing Number Problem in Dimension Three. Discrete Comput Geom 69, 931–935 (2023). https://doi.org/10.1007/s00454-021-00311-6
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DOI: https://doi.org/10.1007/s00454-021-00311-6