Glide plane, diagonal

P2i/nl 1, P12i/nl (or short P2]/n) or PI 12i/n, when the unique two-fold screw axis is chosen to be parallel to X, Y or Z, respectively, but the selection of the diagonal glide plane, n, represents a deviation from the standard. 

Fi y diagonal glide plane, Vz in direction of the arrow at height h b above the plane of the diagram o centre of symmetry... 

The onl other symmetry element involving translation which remains to be meniiqued is the glide plane having a translation of one-quarter of a eell-faee diagonal this type of glide, symbolized d, is found only in a few space-groups. 

In some crystals there is a glide plane n having a translation, not along an axis, but half-way along a face-diagonal of the cell. In fact, the same... 

In a similar way a glide plane normal to the c axis of a crystal having a translation of one-quarter of the ab diagonal (symbolized d) nullifies all hkO reflections except those for which A-j-A is divisible by 4. 

Consider the positions of the titanium atoms. There are only two of these in the unit cell if one is placed at the corner of the unit cell, then the other can only be at the centre of the cell the glide planes having diagonal translation demand it.f... 

The displacement by in the first row and fourth column comes from the mirror reflection in the plane at x = 1/4. The A in the second and third rows of the fourth column are the components of the diagonal glide. The location of the transformed point is that marked by a comma (,) and M>+. The MR of the operation (rry A 0 0)[xyz], when the axial glide plane lies at y=lA, is... 

Pi n is a glide plane perpendicular to axis-i with a diagonal translation... 

Both short and full symbols are used for the space groups. In the latter, both symmetry axes and symmetry planes for each symmetry direction are explicitly designated whereas in the former symmetry axes are suppressed. For example, the short symbol lA/mmm designates a body-centered tetragonal space lattice with three perpendicular mirror planes. One of these mirror planes is also perpendicular to the rotation axis, which is denoted by the slash between the 4 and the first m, while the other two mirror planes are parallel with, or contain, the rotation axis. The full symbol for this space group is lA/m Ijm Ijm 42/n 2i/n 2i/c, which reveals the additional presence of screw axes and a diagonal glide line. 

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