Some notes on tetrahedrally closed spherical sets in Euclidean spaces

  • Bart De BruynEmail author


We describe a connection between a family of tetrahedrally closed spherical sets in Euclidean spaces and a family of point-line geometries called near polygons.


Euclidean space spherical set tetrahedron near polygon 

2010 Mathematics Subject Classification

52C07 52C35 05B25 



The author would like to thank the anonymous referee for his/her valuable comments.


  1. 1.
    Brouwer A E, Cohen A M and Neumaier A, Distance-Regular Graphs (1989) (New York: Springer)CrossRefGoogle Scholar
  2. 2.
    Brouwer A E and Wilbrink H A, The structure of near polygons with quads, Geom. Dedicata 14 (1983) 145–176MathSciNetCrossRefGoogle Scholar
  3. 3.
    Cameron P J, Goethals J-M, Seidel J J and Shult E E, Line graphs, root systems and elliptic geometry, J. Algebra 43 (1976) 305–327MathSciNetCrossRefGoogle Scholar
  4. 4.
    Conway J H and Sloane N J A, Sphere packings, lattices and groups, third edition. Grundlehren der Mathematischen Wissenschaften 290 (1999) (New York: Springer)Google Scholar
  5. 5.
    De Bruyn B, On tetrahedrally closed line systems and a generalization of the Haemers–Roos inequality, preprint (2016)Google Scholar
  6. 6.
    Horn R A and Johnson C R, Matrix analysis, second edition (2013) (Cambridge: Cambridge University Press)Google Scholar
  7. 7.
    Leech J, Notes on sphere packings, Can. J. Math. 19 (1967) 251–267MathSciNetCrossRefGoogle Scholar
  8. 8.
    Neumaier A, Krein conditions and near polygons, J. Comb. Theory Ser. A 54 (1990) 201–209MathSciNetCrossRefGoogle Scholar
  9. 9.
    Shult E E and Yanushka A, Near \(n\)-gons and line systems, Geom. Dedicata 9 (1980) 1–72MathSciNetCrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.Department of MathematicsGhent UniversityGhentBelgium

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