Universal minima of potentials of certain spherical designs contained in the fewest parallel hyperplanes

01/16/2023

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by   Sergiy Borodachov, et al.

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We find the set of all universal minimum points of the potential of the 16-point sharp code on S^4 and (more generally) of the demihypercube on S^d, d≥ 5, as well as of the 2_41 polytope on S^7. We also extend known results on universal minima of three sharp configurations on S^20 and S^21 containing no antipodal pair to their symmetrizations about the origin. Finally, we prove certain general properties of spherical (2m-1)-designs contained in as few as m parallel hyperplanes (all but one configuration considered here possess this property).