Building up a diamond lattice

[EN CONSTRUCCION]

• Consider:

1. a cubic simulation box whose sides are of length $\left.L\right.$
2. a number of lattice positions, $\left.M\right.$ given by $\left.M=8m^{3}\right.$,

with $m$ being a positive integer

• The $\left.M\right.$ positions are those given by:

$\left\{{\begin{array}{l}x_{a}=i_{a}\times (\delta l)\\y_{a}=j_{a}\times (\delta l)\\z_{a}=k_{a}\times (\delta l)\end{array}}\right\}$

where the indices of a given valid site are integer numbers that must fulfill the following criteria

• $0\leq i_{a}<4m$
• $0\leq j_{a}<4m$
• $0\leq k_{a}<4m$,
• the sum of $\left.i_{a}+j_{a}+k_{a}\right.$ can have only the values: 0, 3, 4, 7, 8, 10, ...

i.e, $\left.i_{a}+j_{a}+k_{a}=4n\right.$; OR; Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \left.i_{a}+j_{a}+z_{a}=4n+3\right.} , with $n$ is any integer number

with $\left.\delta l=L/(4m)\right.$