Screw Axes and Glide Planes
Screw axes and glide planes operate in the same way as rotations and mirrors with an extra translation attached. The same rules apply as on the previous pages.
Consider a \(b\) glide plane perpendicular to \(c\) located at \(c = 0\). This will transform the position \((x, y, z)\) to \((x, y+\frac{1}{2}, -z)\). The \(c\) coordinate is made negative by the mirror, while the \(b\) coordinate has \(\frac{1}{2}\) added to it by the \(b\) glide.
Similarly, a \(2_{1}\) screw axis parallel to the \(a\) axis located at \((a, 0, 0)\) would transform the position \((x, y, z)\) to the position \((a+\frac{1}{2}, -b, -c)\). This is the same as a two-fold rotation axis parallel to \(a\), with an extra translation along the \(a\) axis.
Have a go at making up some of your own, determining where the position \((x, y, z)\) would move to under these symmetry elements. Compare these with the view of atoms moving on space group diagrams.