The \(D_4\) Root System is Not Universally Optimal

DSpace/Manakin Repository

The \(D_4\) Root System is Not Universally Optimal

Citable link to this page


Title: The \(D_4\) Root System is Not Universally Optimal
Author: Cohn, Henry; Kumar, Abhinav; Conway, John H.; Elkies, Noam

Note: Order does not necessarily reflect citation order of authors.

Citation: Cohn, Henry, John H. Conway, Noam D. Elkies, and Abhinav Kumar. 2007. The \(D_4\) root system is not universally optimal. Experimental Mathematics 16(3): 313-320.
Full Text & Related Files:
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.
Published Version:
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at
Citable link to this page:
Downloads of this work:

Show full Dublin Core record

This item appears in the following Collection(s)


Search DASH

Advanced Search