The basis is face-centered cubic and is given by $x_1=(0.5,0.5,0)$, $x_2=(0,0.5,0.5)$ and $x_3=(0.5,0,0.5)$.
Two atoms, one at $(0,0,0)$ and the other at $(0.25,0.25,0.25)$ with respect to the basis, generate the Si diamond primitive cell.
The basis is face-centered cubic and is given by $x_1=(0.5,0.5,0)$, $x_2=(0,0.5,0.5)$ and $x_3=(0.5,0,0.5)$.
Two atoms, one at $(0,0,0)$ and the other at $(0.25,0.25,0.25)$ with respect to the basis, generate the Si diamond primitive cell.