Editing Kissing number (section)

===Three dimensions===
In three dimensions, the kissing number is 12, but the correct value was much more difficult to establish than in dimensions one and two. It is easy to arrange 12 spheres so that each touches a central sphere, with a lot of space left over, and it is not obvious that there is no way to pack in a 13th sphere. (In fact, there is so much extra space that any two of the 12 outer spheres can exchange places through a continuous movement without any of the outer spheres losing contact with the center one.) This was the subject of a famous disagreement between mathematicians [[Isaac Newton]] and [[David Gregory (mathematician)|David Gregory]]. Newton correctly thought that the limit was 12; Gregory thought that a 13th could fit. Some incomplete proofs that Newton was correct were offered in the nineteenth century, most notably one by [[Reinhold Hoppe]], but the first correct proof (according to Brass, Moser, and Pach) did not appear until 1953.<ref name=Conway>{{cite book |first=John H. |last=Conway |author-link=John Horton Conway |author2=Neil J.A. Sloane |author-link2=Neil Sloane  |year=1999 |title=Sphere Packings, Lattices and Groups |edition=3rd |publisher=Springer-Verlag |location=New York |isbn=0-387-98585-9|page=[https://books.google.com/books?id=upYwZ6cQumoC&pg=PA21 21]}}</ref><ref  name=Brass>{{cite book |first1=Peter |last1=Brass |first2=W. O. J. |last2=Moser |first3=János |last3=Pach |author-link3=János Pach |title=Research problems in discrete geometry |publisher=Springer |year=2005 |isbn=978-0-387-23815-9 |page=[https://books.google.com/books?hl=en&id=cT7TB20y3A8C&pg=PA93 93]}}</ref><ref>{{cite book
 | last = Zong | first = Chuanming
 | editor1-last = Goodman | editor1-first = Jacob E.
 | editor2-last = Pach | editor2-first = J├ínos
 | editor3-last = Pollack | editor3-first = Richard
 | contribution = The kissing number, blocking number and covering number of a convex body
 | doi = 10.1090/conm/453/08812
 | location = Providence, RI
 | mr = 2405694
 | pages = 529–548
 | publisher = American Mathematical Society
 | series = Contemporary Mathematics
 | title = Surveys on Discrete and Computational Geometry: Twenty Years Later (AMS-IMS-SIAM Joint Summer Research Conference, June 18ÔÇô22, 2006, Snowbird, Utah)
 | volume = 453
 | year = 2008| isbn = 9780821842393
 }}.</ref>

The twelve neighbors of the central sphere correspond to the maximum bulk [[coordination number]] of an atom in a [[crystal lattice]] in which all atoms have the same size (as in a chemical element). A coordination number of 12 is found in a [[cubic close-packed]] or a [[hexagonal close-packed]] structure.