Building up a face centered cubic lattice

• Consider:

1. a Cubic Simulation box of length $L$
2. a number of lattice positions, $M$ given by:

$M=4m^3$

with $m$ being a positive integer

• The $M$ positions are those given by:

$\{\begin{array}{c}{x}_a=i_a\times (\delta l)\\ y_a=j_a\times (\delta l)\\ z_a=k_a\times (\delta l)\end{array}\}$

where the indices of a given valid site are integer number that must fulfill:

• $0\le i_a<m$
• $0\le j_a<m$
• $0\le k_a<m$,

and its sum: $i_a+j_a+k_a$ must be an, for instances, even number.

with $\delta l=L/(2m)$