= Solution
Reduce the supplied fractional coordinates modulo one. The <rutile structure> has Ti at $(0,0)$ with height $z=0$ and at $(1/2,1/2)$ with height $z=1/2$. The oxygen projections are $(0.30,0.30),(0.70,0.70)$ at $z=0$, and $(0.80,0.20),(0.20,0.80)$ at $z=1/2$. Include equivalent corner sites to show the boundary of a complete <unit cell>; the cell edges are $a$ along $[100]$ and $[010]$.
\Image[/past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2022/paper-1-rutile.png]
{title=Rutile unit-cell projection along the tetragonal axis}
{description=Original plan constructed from the fractional coordinates. Labels give height as a fraction of $c$; circle sizes distinguish species rather than ionic radii.}
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