Editing Half-integer (section)

===Sphere packing===
The densest [[lattice packing]] of [[unit sphere]]s in four dimensions (called the [[D4 lattice|''D''<sub>4</sub> lattice]]) places a sphere at every point whose coordinates are either all integers or all half-integers. This packing is closely related to the [[Hurwitz integer]]s: [[quaternion]]s whose real coefficients are either all integers or all half-integers.<ref>{{cite journal |first=John C. |last=Baez |authorlink=John C. Baez |year=2005 |title=Review ''On Quaternions and Octonions: Their geometry, arithmetic, and symmetry'' by John H. Conway and Derek A. Smith |type=book review |journal=Bulletin of the American Mathematical Society |volume=42 |pages=229–243 |url=http://math.ucr.edu/home/baez/octonions/conway_smith/ |doi=10.1090/S0273-0979-05-01043-8 |doi-access=free}}</ref>