= Solution
Successive planes normal to $[001]$ are chemically ordered Au and Cu layers. The supplied four-site cell is a convenient doubled description of the \b[<primitive tetragonal lattice>]: valid primitive translations are
$$
\mathbf a_1=\tfrac a2(1,1,0),\quad
\mathbf a_2=\tfrac a2(-1,1,0),\quad
\mathbf a_3=(0,0,c).
$$
They give a square basal cell of side $a/\sqrt2$, containing an Au basis atom at the origin and Cu at fractional $(1/2,1/2,1/2)$. That last vector exchanges chemical species and is not a Bravais translation. Thus a face-centred-looking atomic arrangement does not make the chemically ordered material an FCC <Bravais lattice>. This is the <L10 crystal structure>; the following indices retain the larger cell specified in the question.
\Image[/past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2019/paper-1-cuau-plan.png]
{title=Ordered copper-gold structure viewed along the second basal axis}
{description=Original two-by-two projection of the supplied four-site cell. Colour gives chemical species; labels distinguish the fractional coordinate along the viewing direction.}
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