Problem $4$

A material shown below has a cubic crystal structure with eight atoms centered at each corner of each cube $($shown in red$),$ six atoms centered each face of the cube $($shown in blue$)$ and one atom centered at the center of the cube $($shown in green$).$ List the point indices for each of the $15$ atoms. The corner atoms are labeled $1-8,$ the face atoms are labeled $9-14,$ and the atom at the center is labeled $15.$