The Wigner-Seitz cell is not really a direct measure of interatomic distances. It is more a description of the volume of points closest to a lattice point. If you take a 2D square lattice, the Wigner Seitz cell is a square of identical cell dimensions, centered around each lattice point. If you take a rectangular 2D cell, the W-S cell is also a rectangle of identical unit cell length, centered around each lattice point. As the dimensions of the rectangular unit cell change, so do those of the W-S cell.  If you change the aspect ratio, those of th W-S cell will follow. Thus the borders of the W-S cell are at different distances to the central atom even for something as basic as a 2-D lattice.

To calculate the distance from any atom to another in a triclinic unit cell, you will have to calculate the value of  the vector product: square root of (u*G*u), where u is the vector with the fractional coordinates, and G the metric tensor. The first u is the transposed from i.e. the row vector (x,y,z) the second u the column vector. The elements of the metric tensor are pairwise scalar products of the base vectors.

G(1,1) = a*a

G(1,2) = a*b*cos(gamma) etc.

Most programs that visualize crystal structure can calculate interatomic distances. JMOL is a free one for example

As R. B. Neder mentionned it the Wigner-Seitz cell is nots usually used to calculate the interatomic distances or the number of nearrest atoms neighbor.

One will correct me if I'm wrong but, the way the wigner-seitz cell is constructed we may deduce the number of nearest neighbor by the number of the closest planes delimiting the W-S volume (as they should be equal).

I guess you can used AtomEye to see the number of nearest neighbor processing as follow : 1 you load your structure on AE  __2 you flag one atom __3 you add a filter that only shows the atoms which are under a certain distance from the flagged one (distance that you can increase or decrease) OR you can add a filter which only draw the bond under a certain length (length that you precise). You just have to count the bond of a specific atom of your structure.

Actually the question is not clear. If, as already noted above, one wants to know the distances of atoms from a given atom it is necessary to have the atomic coordinates of the atoms within the unit cell of a crystalline material. The process is not straightforward and to understand it one must know at least basic crystallography.

Hi R. B.Neder, Matthieu David and Giovanni Ferraris, thank you very much for your answers. I know there are a lot of software to visualise the crystal structure. It is also easy to measure atomic distances, bond angles, and so on. But the problem is: how to define the nearest neighbours, next nearest neighbours. As mentioned by Giovanni Ferraris, certain length is required to distinguish nearest neighbours from next nearest neighbours, next next nearest neighbours. How to determine such "certain length"?