= Solution
The <zinc blende structure> has an FCC <sulfur> sublattice and <zinc> on half its tetrahedral sites. One conventional <unit cell> uses S at $(0,0,0),(1/2,1/2,0),(1/2,0,1/2),(0,1/2,1/2)$ and Zn at those positions displaced by $(1/4,1/4,1/4)$, reduced modulo one. The <wurtzite structure> has ABAB <sulfur> layers, instead of ABCABC layers. One hexagonal-cell convention uses S at $(0,0,0),(2/3,1/3,1/2)$ and Zn at $(0,0,u),(2/3,1/3,1/2+u)$, with ideal $u=3/8$. Looking along $[001]$ superposes S and Zn in that latter coordinate convention; the height labels distinguish them.
\Image[/past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2019/paper-1-zns-projections.png]
{title=Two-by-two zinc sulfide unit-cell projections along the stacking axes}
{description=Original coordinate constructions. Heights are fractional coordinates along the viewing axis. The hexagonal plan uses basal vectors at 120 degrees.}
The closest-packed <sulfur> planes are \b[$\{111\}$, with four distinct plane orientations], for <zinc blende structure>, and \b[$\{001\}$, with one orientation], for <wurtzite structure>. Opposite normals describe the same unoriented plane orientation. Hexagonal four-index notation writes the latter basal family as $\{0001\}$.
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