[T]he best packings in up to eight dimensions belong to families <math>A_n, D_n </math> and <math>E_n</math>, and the corresponding s turn up in appa… - John Horton Conway

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[T]he best packings in up to eight dimensions belong to families <math>A_n, D_n </math> and <math>E_n</math>, and the corresponding s turn up in apparently unrelated areas... [I]n 24 dimensions the <math>\Lambda_{24}</math> has... connections with , s, and the Monster simple group... [O]ne day someone will write an article on "The Ubiquity of the Leech lattice." ...There are applications of... packings to number theory... [e.g.,] solving s, and to "the "... There are... applications of sphere packings... in digital communications... a typical question from... spread-spectrum communications for mobile radio... how many spheres of radius 0.25 can be packed in a sphere of radius 1 in 100-dimensional space? ...Two and three-d... packings... circles in a two-d... packing may represent s... in... a cable. Three-d... packings have applications in chemistry and physics... biology... antenna design... choosing directions for X-ray tomography... and... statistical analysis on spheres... n-dimensional packings may be used in... numerical evaluation of integrals... on the surface of a sphere in <math>\R^n</math> or in its interior. ...A related application ...n-dimensional search or approximation problems ...[I]n physics... dual theory and superstring theory... have involved the <math>E_8</math> and <math>\Lambda_{24}</math> lattices and the related Lorentzian lattices in dimensions 10 and 26...