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A screw axis combines rotation about a line with translation parallel to that line. An $n_p$ screw rotates through $2\pi /n$ and advances by $p/n$ of the lattice repeat along the axis; a $2_1$ screw advances by half a repeat after a half-turn. The combined operation, rather than either component separately, must map every atomic species onto equivalent sites.

A glide plane combines reflection in a plane with a fractional translation parallel to it. Reflecting alone need not preserve the crystal. A crystallographic point symmetry is an isometry with a fixed point, such as a rotation, reflection, inversion, or rotoinversion. Point operations have no irreducible translational advance: a screw or a glide with nonzero fractional advance cannot be described merely as a rotation or mirror at a different origin. A crystal's point group records the rotational parts of its space-group operations, whereas the full space group retains their translations.

One crystallographic inversion center isThe inversion maps $(x,y,z)$ to $(1/2-x,1/2-y,-z)$; it exchanges both the Fe pair and the Se pair modulo lattice translations.

A $\bar{4}$ axis passes along $z$ through the Fe site $(0,0,0)$, and likewise through $(1/2,1/2,0)$. A representative rotoinversion isIt leaves the first Fe site fixed, maps the other Fe onto a translationally equivalent site, and exchanges the Se height classes. The $\bar{4}$ operation includes a vertical reversal, so it must not be replaced by a pure $90$-degree rotation about an Fe site. Such a pure rotation would put a selenium atom at the wrong height.