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

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dc.contributor.author	Cohn, Henry
dc.contributor.author	Kumar, Abhinav
dc.contributor.author	Conway, John H.
dc.contributor.author	Elkies, Noam
dc.date.accessioned	2009-04-13T16:34:27Z
dc.date.issued	2007
dc.identifier.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.	en
dc.identifier.issn	1058-6458	en
dc.identifier.uri	http://nrs.harvard.edu/urn-3:HUL.InstRepos:2794814
dc.description.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.	en
dc.description.sponsorship	Mathematics	en
dc.publisher	AK Peters	en
dc.relation.isversionof	http://akpeters.metapress.com/content/n1700h637u4tk136	en
dash.license	LAA
dc.title	The \(D_4\) Root System is Not Universally Optimal	en
dc.relation.journal	Experimental mathematics	en
dash.depositing.author	Elkies, Noam