24維空間中，單位球周圍最多能有多少個不互相重合的單位球與之相切？

這就是經典的Kissing Number問題，我們只知道1,2,3,4,8,24維的結果，24維的Kissing Number是196,560，被Leech Lattice實現。

Kissing number problem

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In geometry, a kissing number is defined as the number of non-overlapping unit spheres that can be arranged such that they each touch another given unit sphere. For a lattice packing the kissing number is the same for every sphere, but for an arbitrary sphere packing the kissing number may vary from one sphere to another. Other names for kissing number that have been used are Newton number (after the originator of the problem), andcontact number.

In general, the kissing number problem seeks the maximum possible kissing number for n-dimensional spheres in (n + 1)-dimensionalEuclidean space. Ordinary spheres correspond to two-dimensional closed surfaces in three-dimensional space.

Finding the kissing number when centers of spheres are confined to a line (the one-dimensional case) or a plane (two-dimensional case) is trivial. Proving a solution to the three-dimensional case, despite being easy to conceptualise and model in the physical world, eluded mathematicians until the mid-20th century.[1][2] Solutions in higher dimensions are considerably more challenging, and only a handful of cases have been solved exactly. For others investigations have determined upper and lower bounds, but not exact solutions.[3]