I am reading Ashcroft and Mermin and, to define coordination number, they use the notion of nearest neighbours which they do not define. I'm sure it's a very trivial definition, but they had been so precise up until now so I wanted to be sure. After searching "definition of nearest neighbours" in Google and looking at Kittel and Simon, I still don't have an answer.
How are "nearest neighbours" defined in a Bravais lattice? I assume a possible definition is the naive one: fix an arbitrary point in the lattice, call it $x$. Given the set of all other points in the Bravais lattice, there will exist points such that $d(x,y)$ is minimized (where $d$ is the usual metric and $y$ is any point other than $x$); call this minimum value $\alpha$. Then a nearest neighbour is any point $y$ in the lattice with $d(x,y)=\alpha$.
The definition can doubtless be made more slick, but I'm just hoping for confirmation that it's correct.