= Solution
An ideal cubic <perovskite structure> is obtained by putting \b[La at the cube corners, Re at the body center, and N at the face centers]. In <fractional crystal coordinates> one convenient basis is
$$
\mathrm{La}:(0,0,0),\qquad
\mathrm{Re}:(\tfrac12,\tfrac12,\tfrac12),\qquad
\mathrm N:(\tfrac12,\tfrac12,0),(\tfrac12,0,\tfrac12),(0,\tfrac12,\tfrac12).
$$
The counting is $8/8=1$ La, one Re and $6/2=3$ N per cell. Corner-sharing $\mathrm{ReN_6}$ <octahedra> form the network, with La in the larger interstices. The ideal cell illustrates the connectivity; octahedral tilting can lower the actual <crystal symmetry>.
\Image[/past-exam-of-the-chemistry-course-of-the-year-4-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1-perovskite.png]
{title=Ideal perovskite connectivity for lanthanum rhenium nitride}
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