= Solution
The <fluorite structure> consists of a <face-centered cubic lattice> of <calcium> sites with all eight <tetrahedral interstitial sites> occupied by <fluoride>. In fractional coordinates of the conventional cubic <unit cell>, the <calcium> basis is $(0,0,0),(0,\tfrac12,\tfrac12),(\tfrac12,0,\tfrac12),(\tfrac12,\tfrac12,0)$, and <fluoride> occupies all combinations $(x,y,z)$ with $x,y,z\in\{\tfrac14,\tfrac34\}$. The projection therefore superposes two <fluoride> sites at each quarter-coordinate position. Labels in the original diagram give fractional depth along $[001]$; periodic boundary sites are displayed on both edges.
\Image[/past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2017/paper-1-fluorite.png]
{title=Original fluorite projection along the cubic z axis with fractional depths and the limiting anion-contact geometry}
Counting shared sites gives $8/8+6/2=4$ <calcium> sites and eight interior <fluoride> sites: \b[four <formula units> per conventional cell].
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