Editing Packing problems (section)

===Sphere packings in higher dimensions===
{{Main|Sphere packing}}

In three dimensions, [[Close-packing of spheres|close-packed]] structures offer the best ''lattice'' packing of spheres, and is believed to be the optimal of all packings. With 'simple' sphere packings in three dimensions ('simple' being carefully defined) there are nine possible definable packings.<ref>{{cite journal | last1 = Smalley | first1 = I.J. | year = 1963 | title = Simple regular sphere packings in three dimensions | journal = Mathematics Magazine | volume = 36 | issue = 5| pages = 295–299 | doi = 10.2307/2688954 | jstor = 2688954 }}</ref> The 8-dimensional [[E8 lattice]] and 24-dimensional [[Leech lattice]] have also been proven to be optimal in their respective real dimensional space.