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I think that the Fe-I sites have all 4-fold symmetry (rotations of 90° in all directions return the same crystal). I also “see” some 3-fold symmetries when rotating around the edges, focusing on the Fe-II sites (i.e., performing 2x 60° = 120° rotations). Thus, eta is always zero.
For the Fe-II sites, the axis perpendicular to the plane ( are Fe-IIa, Fe-IIb, Fe-IIa, fe-IIb) is 4-fold, while the axis identifying that plane have a different symmetry… 2-fold? So, eta is not always equal to zero.
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