Kissing number

Summary

The kissing number $\tau(n)$ is the largest number of non-overlapping unit balls in $\R^n$ that can all touch one central unit ball. It is known exactly only in dimensions $1$, $2$, $3$, $4$, $8$ and $24$, where it equals $2$, $6$, $12$, $24$, $240$ and $196560$. The problem is a close relative of sphere packing and of the theory of spherical codes.