Mathematics – Metric Geometry
Scientific paper
2006-07-19
Experimental Mathematics 16 (2007), 313-320
Mathematics
Metric Geometry
11 pages, updated to incorporate small changes in published version
Scientific paper
10.1080/10586458.2007.10129008
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.
Cohn Henry
Conway John H.
Elkies Noam D.
Kumar Abhinav
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