The D_4 root system is not universally optimal
Metric Geometry
2012-03-15 v3
Abstract
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.
Cite
@article{arxiv.math/0607447,
title = {The D_4 root system is not universally optimal},
author = {Henry Cohn and John H. Conway and Noam D. Elkies and Abhinav Kumar},
journal= {arXiv preprint arXiv:math/0607447},
year = {2012}
}
Comments
11 pages, updated to incorporate small changes in published version