Henry Cohn, John H. Conway, Noam D. Elkies, Abhinav Kumar
Published 2006-07-19, updated 2008-09-09Version 3
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.
Comments: 11 pages, updated to incorporate small changes in published version
Journal: Experimental Mathematics 16 (2007), 313-320
Towards a proof of the 24-cell conjecture
Optimality and uniqueness of the D_4 root system
The $E_t$-Construction for Lattices, Spheres and Polytopes
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