Glide planes

Consider now the restrictions imposed by the periodicity on the translation component t of a glide plane. The glide plane will coincide with a crystallographic plane and the glide direction with a lattice row (parallel to the plane). Let  t be the glide vector and T the periodicity of the lattice row to which the glide direction is parallel; if we apply the glide operation twice, the result will be a translation 2t . In order to mantain the periodicity of the crystal we must have:

2 t = p T , with integer p

or

t = (p/2) T

As p varies over all integer values, the following translations are obtained: 0 T, (1/2) T, T, (3/2) T, .....of which only the first two are distinct.

For p=0 the glide plane reduces to a mirror m.

Glides with translational components equal to a/2, b/2, c/2 are indicated by a, b, c respectively; diagonal glides with translational components (a+b)/2, (a+c)/2, (b+c)/2, (a+b+c)/2 are indicated by n.

For a non primitive unit cell the vector T may be a lattice vector with rational components indicated by the symbol d .