Return link to the symbol table

The first symbol above shows the position of a point (or atom or molecule)
within the unit cell. The "+" sign represents the height +*z*.
An open circle indicates a particular handedness for this point.
In each space group diagram, the bottom left-hand region of the unit cell
has been chosen for
the position of an initial point with coordinates *x*,*y*,*z*.
Symmetry equivalent positions are shown relative to this initial point.

The second symbol represents a point
related by symmetry to the initial point, but now at a height 1/2+*z*.
As an open circle, it has the same handedness as the initial point.
Thus, in this instance, it is related either by a screw axis
parallel to Z or by a lattice translation to the initial point.

The ""
in the third symbol indicates a change of handedness with respect
to the initial point due to the presence of either a rotary-inversion axis or
a plane within the space group. Note that height of the point is now
-*z*.
The fourth symbol shows a symmetry equivalent point of the opposite handednes
and height 1/4-*z*.

Finally, certain symmetry operations will result in two symmetry equivalent
points being superimposed in the space group diagram.
Thus a mirror plane in the plane of the screen
will reflect the initial point from +*z* to -*z* with
a change of handedness, but without any change in the
*x*,*y* coordinates
of the point. The effect of this is shown in the fifth symbol where the
right-half might represent the initial point and the left-half is the symmetry
equivalent position resulting from the operation of the mirror acting in the
XY plane.

© Copyright 1997-1999. Birkbeck College, University of London.