= Solution
The <vertical mirrors of the diamond cubic structure> have the required orientation: their normals lie in the $(001)$ plane. In the chosen atomic-origin convention, their traces satisfy
$$
\boxed{x-y=\frac n2,\qquad x+y=\frac n2,\qquad n\in\mathbb Z,}
$$
with $x,y$ expressed as fractions of $a$. These are the two orientations of vertical $\{110\}$ mirrors and their translated copies. For example, the plane $x=y$ interchanges the first two coordinates and leaves every <diamond> site in an equivalent site. <Reflection> in $x+y=1/2$ sends $(x,y,z)$ to $(1/2-y,1/2-x,z)$, which also preserves the full three-dimensional motif.
The projected traces alone do not test a mirror: the atom heights must also agree under <reflection>. In particular, a vertical $\{100\}$ trace can appear plausible in an unlabelled projection but does not preserve all heights as a pure mirror; glide operations are different symmetry elements.
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