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

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Abstract.

We prove that on the Euclidean sphere S 3 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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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 G. Bonchev str., Sofia 1113, Bulgaria, peter@moi.math.bas.bg, , , , , , BG

    P. Boyvalenkov

  2. Dept. of Electrical Engineering, Linköping University, SE-581 83 Linköping, Sweden, danyo@isy.liu.se, , , , , , SE

    D. Danev

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  1. P. Boyvalenkov
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  2. D. Danev
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Eingegangen am 7.2.2000

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Boyvalenkov, P., Danev, D. Uniqueness of the 120-point spherical 11-design in four dimensions. Arch. Math. 77, 360–368 (2001). https://doi.org/10.1007/PL00000504

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  • DOI: https://doi.org/10.1007/PL00000504

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