The number of equivalent hyperspheres in dimensions which can touch an equivalent hypersphere without any intersections, also sometimes called the Newton number, contact number, coordination number, or ligancy. Newton correctly believed that the kissing number in three dimensions was 12, but the first proofs were not produced until the 19th century (Conway and Sloane 1993, p. 21) by Bender (1874), Hoppe (1874), and Günther (1875). More concise proofs were published by Schütte and van der Waerden (1953) and Leech (1956). After packing 12 spheres around the central one (which can be done, for example, by arranging the spheres so that their points of tangency with the central sphere correspond to the vertices of an icosahedron), there is a significant amount of free space left (above figure), although not enough to fit a 13th sphere.

Exact values for lattice packings are known for to 9 and (Conway and Sloane 1992, Sloane and Nebe). Odlyzko and Sloane (1979) found the exact value for 24-D.

The arrangement of points on the surface of a sphere, corresponding to the placement of identical spheres around a central sphere (not necessarily of the same radius) is called a spherical packing.

The following table gives the largest known kissing numbers in dimension for lattice () and nonlattice (NL) packings (if a nonlattice packing with higher number exists). In nonlattice packings, the kissing number may vary from sphere to sphere, so the largest value is given below (Conway and Sloane 1993, p. 15). A more extensive and up-to-date tabulation is maintained by Sloane and Nebe.

OMG,牛顿数，有关n维空间中可与单元球接触的等体积球数，这个要翻译起来可需要好长时间了。

费了半天劲，看看下面的翻译行吗？自己再组织一下语言，在这里要找一个精通几何又通英文的人基本上没可能啊，这样的人哪有空上网啊。
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在能接触相等的超球面的尺寸方面的等效的超球面的数量， 叫牛顿数，联络数，协作数或者ligancy。

牛顿确信3 维的牛顿数是12， 但是第一个证据直到19世纪才做出来（Conway and Sloane 1993，第21页， 作者：Bender (1874),Hoppe (1874) ,以及Gunther(1875)）。更简明的证据由Schutte和Van der Waerden(1953)及Leech(1956)提出.

在把12个球体围在中心之后(哪个可以被做，例如，通过安排领域， 以便他们的有中心的领域的tangency的点相当于icosahedron的顶点),有相当多数量的(高于数字)留下的下自由空间 ,虽然不得足以适合第13个球体。

包装的格子的精确值对9和(Conway and Sloane 1992，Sloane and Nebe)而闻名.Odlyzko和Sloane(1979)找到24-D的精确值

一个领域的表面上的点的安排， 在中心领域周围的相当于对相同球面的安排(不一定相同半径) 被叫做球体表面。

那些下述表格给最大的已知的牛顿数的大小及数目() 以及nonlattice(NL) 球面(如果充满更高的数目的nonlattice存在) . 在球包着的nonlattice过程中，牛顿数可以因领域而不同，因此最大的价值被在(Conway and Sloane 1993，第15页),

更广的，到目前为止的表是由Sloane和Nebe保持的。