# The $$D_4$$ Root System is Not Universally Optimal

 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

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