# Matrices of simple face and cubic centered cubic lattice

## Main Question or Discussion Point

$$S= \begin{bmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{bmatrix}$$

for simple cubic

$$I= \begin{bmatrix} -\frac{a}{2} & \frac{a}{2} & \frac{a}{2} \\ \frac{a}{2} & -\frac{a}{2} & \frac{a}{2} \\ \frac{a}{2} & \frac{a}{2} & -\frac{a}{2} \end{bmatrix}$$

for volume centered cubic

$$F= \begin{bmatrix} 0 & \frac{a}{2} & \frac{a}{2} \\ \frac{a}{2} & 0 & \frac{a}{2} \\ \frac{a}{2} & \frac{a}{2} & 0 \end{bmatrix}$$

for face centered cubic

I don't see any logic for this matrices? How can I get this? I can axcept that simple is P because minimum distance between neighbors is $$a$$. But But what with the other two matrices?

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