Around the Na at fractional (0,0,0), determine separately (a) the closest Cl shell and (b) the closest noncentral Na shell. Report each distance and population, identify the first-shell coordination polyhedron, and explain why counting only basis atoms in the displayed cell can give a wrong population.

Use the supplied periodic conventional cubic cell, not an isolated XYZ cluster. Cartesian XYZ coordinates are in angstrom; 1 nm=10 angstrom. XYZ atom rows start at one after the two header lines. Fractional positions below are exact; each listed basis atom has occupancy 1. Cell vectors are (a,0,0),(0,a,0),(0,0,a); all angles90 degrees. Crystal images are r_j+a*(n_x,n_y,n_z) for integer n. No relaxation, defects, thermal motion or finite crystallite envelope is supplied.
halite S0008: a=5.64056 angstrom. Row / element / fractional x,y,z:
1 Na 0 0 0
2 Na 0 1/2 1/2
3 Na 1/2 0 1/2
4 Na 1/2 1/2 0
5 Cl 0 0 1/2
6 Cl 0 1/2 0
7 Cl 1/2 0 0
8 Cl 1/2 1/2 1/2

Search translations n_x,n_y,n_z in {-1,0,1}, excluding the central Na itself. Treat distinct periodic images as distinct neighbors; use 0.00001 angstrom shell tolerance. Report distances in nm to four decimals. Identify first-shell directions with displacement vectors or axis signs.

Attachment S0008:
8
Coordinates in angstrom; atoms numbered from 1.
Na 0.00000000 0.00000000 0.00000000
Na 0.00000000 2.82028000 2.82028000
Na 2.82028000 0.00000000 2.82028000
Na 2.82028000 2.82028000 0.00000000
Cl 0.00000000 0.00000000 2.82028000
Cl 0.00000000 2.82028000 0.00000000
Cl 2.82028000 0.00000000 0.00000000
Cl 2.82028000 2.82028000 2.82028000