Sodium chloride crystal,

I am studying the potential electric of a sodium chloride crystal, where the actors says:

To evaluate the potential energy we first observe that every positive
ion is in a position equivalent to that of every other positive ion. Furthermore,
although it is perhaps not immediately obvious from Fig. 1.7, the
arrangement of positive ions around a negative ion is exactly the same as
the arrangement of negative ions around a positive ion, and so on. Hence
we may take one ion as a center, it matters not which kind, sum over its
interactions with all the others, and simply multiply by the total number
of ions of both kinds. This reduces the double sum in Eq. (1.15) to a single
sum and a factor N; we must still apply the factor 1/2 to compensate
for including each pair twice. That is, the energy of a sodium chloride
lattice composed of a total of N ions is

I am not sure if i am getting it, so he gives the formula:
$N/2 sum frac{kq_{1}q_{k}}{r_{1k}}$

So basically, interpreting the formula, it is saying that the central ion is equal to, for example, the potential of the ions on the corner? Is not this wrong?