# Glide Planes

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```					Glide Planes
Glide Planes
Where screw axes can be constructed from any
proper rotation axis and a translation along that
axis, glide planes are only possible with mirror, m,
operations.

However, glide planes have a much richer
combination of possible translations both parallel
and in some special circumstances perpendicular
to the mirror plane.
Axial glide planes restrict the translation vector to ½ unit cell translation
along one of the unit cell axes parallel to the reflection plane.

 1 0 0  x   1 2   1 2  x 
m001 |   1 ,0,0r  0 1 0  y    0    y 
2                                     
0 0  1  z   0   z 
                          
The translation vector for a diagonal glide, n−glide, has components in two
or in special cases even three directions. In most cases the translations
are (a+b)/2, (b+c)/2, or (a+c)/2, but in special situations (tetragonal and
cubic systems) the translation may be (a+b+c)/2.

 1 0 0  x   1 2   1 2  x 
m001 |   1 , 1 ,0r  0 1 0  y    1 2    1 2  y 
2 2                                        
0 0  1  z   0   z 
                             
The translation vector for a diamond glide, d-glide, may also have
components along 2 or even three directions. In most cases the
translations are (a±b)/4, (b±c)/4, or (a±c)/4, but in special situations
(tetragonal and cubic systems) the translation may also be (a±b±c)/4

 1 0 0  x   1 4   1 4  x 
m001 |   1 , 1 ,0r  0 1 0  y    1 4    1 4  y 
4 4                                        
0 0  1  z   0   z 
                             
Several Glides Making up a Space Group
Taking a closer look shows that the symmetry operators in this space
group (which are mostly glides and screws) do not intersect at the origin,
but are displaced. This is true of many of the nonsymmorphic groups.

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