= Solution
The <fluorite structure> has Ce on the corner and face-centre sites of a <face-centered cubic lattice>. Oxygen occupies all eight positions $(x,y,z)$ with each coordinate independently $1/4$ or $3/4$. In projection, there are four oxygen positions $(1/4,1/4),(1/4,3/4),(3/4,1/4),(3/4,3/4)$, each representing two heights. Accounting for shared boundary sites gives \b[four Ce and eight O per conventional <unit cell>].
\Image[/past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2022/paper-1-fluorite.png]
{title=Fluorite unit-cell projection with oxygen heights distinguished}
{description=Original coordinate-based plan; each oxygen marker represents heights $1/4$ and $3/4$. Cerium edge-centre and face-centre heights are labelled.}
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