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Note on packings in Grassmannian space G(3,1)

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Abstract

How must 2N non-overlapping equal circles forming antipodal pairs be packed on a sphere so that the angular diameter of the circles will be as great as possible? In this note, some unnoticed putative solutions to this problem are mentioned, and attention is called to the Danzerian rigidity of the graphs of locally optimal antipodal packings.

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References

  1. J.H. Conway, R.H. Hardin and N.J.A. Sloane, Packing lines, planes, etc.: Packings in Grassmannian spaces, Experiment. Math. 5 (1996) 139–159.

    Google Scholar 

  2. L. Danzer, Endliche Punktmengen auf der 2-Sphäre mit möglichts grossem Minimalabstand, Habilitationsschrift, Universität Göttingen (1963); English translation: Finite point-sets on S2 with minimum distance as large as possible, Discrete Math. 60 (1986) 3–66.

    Article  Google Scholar 

  3. L. Fejes Tóth, Regular Figures (Pergamon, MacMillan, New York, 1964).

    Google Scholar 

  4. L. Fejes Tóth, Distribution of points in the elliptic plane, Acta Math. Acad. Sci. Hungar. 16 (1965) 437–440.

    Article  Google Scholar 

  5. H. Rutishauser, Über Punktferteilungen auf der Kugel-fläche, Comment. Math. Helv. 17 (1945) 327– 331.

    Google Scholar 

  6. K. Schütte und B.L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 order 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951) 96–124.

    Article  Google Scholar 

  7. J. Strohmajer, Über die Verteilung von Punkten auf der Kugel, Ann. Univ. Sci. Budapest. Sect. Math. 6 (1963) 49–53.

    Google Scholar 

  8. T. Tarnai and Zs. Gáspár, Improved packing of equal circles on a sphere and rigidity of its graph, Math. Proc. Cambridge Philos. Soc. 93 (1983) 191–218.

    Article  Google Scholar 

  9. T. Tarnai and Zs. Gáspáar, Packing of equal circles in the elliptic plane and in special domains of the Euclidean plane, in: 3rd Geometry Festival. Int. Conf. on Packings, Coverings and Tilings, Budapest (1996).

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Tarnai, T. Note on packings in Grassmannian space G(3,1). Journal of Mathematical Chemistry 23, 415–419 (1998). https://doi.org/10.1023/A:1019193829804

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