Archiv der Mathematik

, Volume 77, Issue 4, pp 360–368

Uniqueness of the 120-point spherical 11-design in four dimensions


  • P. Boyvalenkov
    • Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 G. Bonchev str., Sofia 1113, Bulgaria,
  • D. Danev
    • Dept. of Electrical Engineering, Linköping University, SE-581 83 Linköping, Sweden,

DOI: 10.1007/PL00000504

Cite this article as:
Boyvalenkov, P. & Danev, D. Arch. Math. (2001) 77: 360. doi:10.1007/PL00000504


We prove that on the Euclidean sphere S3 there exist a unique up to isometry 120-point spherical 11-design and a maximal (4, 120, \( cos(\pi/5) \))-code. Both these are nothing but copies of a famous regular polytope in four dimensions – the 600-cell.

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© Birkhäuser Verlag, Basel 2001