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The D_4 root system is not universally optimal

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arxiv math/0607447 v3 pith:ZWVTWSLM submitted 2006-07-19 math.MG

Henry Cohn , John H. Conway , Noam D. Elkies , Abhinav Kumar This is my paper · ORCID
classification math.MG
keywords optimalrootsystemuniversallycodepointssphericalcell
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We prove that the D_4 root system (equivalently, the set of vertices of the regular 24-cell) is not a universally optimal spherical code. We further conjecture that there is no universally optimal spherical code of 24 points in S^3, based on numerical computations suggesting that every 5-design consisting of 24 points in S^3 is in a 3-parameter family (which we describe explicitly, based on a construction due to Sali) of deformations of the D_4 root system.

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  1. Optimal measures for p-frame energies on spheres

    math.MG 2019-08 accept novelty 8.0 of 10

    Tight designs minimize p-frame energies over all probability measures for p between consecutive even integers, and the 600-cell does so on S3 for p in [8,10].

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