= Solution
Reflection through $z=0$ interchanges the two Se height classes but, by itself, leaves their projected positions wrong. The required parallel translation is
$$
\boxed{\mathbf t_g=(\tfrac12,\tfrac12,0),\qquad
(x,y,z)\mapsto(x+\tfrac12,y+\tfrac12,-z).}
$$
For example, $(1/2,0,\eta)$ maps to $(1,1/2,-\eta)$, equivalent to the second Se site. The two Fe sites are also interchanged. This is a diagonal, or $n$, glide; adding an integer lattice vector gives the same fractional translation class. Its translation is expressed in the conventional <primitive tetragonal lattice> coordinates, not in a smaller Fe-only cell that would discard the selenium height pattern.
Back to article page
