Dialog Box: Symmetry Element Display [ 3D Display Parameters dialog]
In the 3D Display Mode, rotation axes and mirror planes may optionally be shown.
Rotation axes can be shown as simple lines, or cylinders of the specified radius . The standard symbol for each axis, in a 3-dimensional, "extruded" form, will be shown on each end of the axis.
All rotation axes will be the same Color.
Mirror planes are actually shown as plates of the specified Thickness .
If the Opacity is greater than 0.99, they are drawn as totally opaque, which is faster. The planes may be circular or disk shape, or square. Note that the circular outline of disks always consists of line segments, and the number of such segments in VRML files is determined by the viewer, not SHAPE. Thus disks may have an unacceptably polygonal appearance in some VRML file viewers.
Transparency of mirror planes is something of an approximation. Some color combinations for background, crystal edges, faces and mirror planes may work better than others.
Scale factors. These factors determine the relative sizes of the symmetry elements and the crystal. In the Maximize size for each view and Universal maximum scaling modes (Scaling dialog, Input2 menu), the drawing is scaled to the minimum dimension of the screen or the frame for printed or file output. When symmetry elements are shown, it is generally best to reduce the scale of the crystal relative to them. The rotation axes should usually be largest, so that the symbols at the ends are not obscured. If they are given scale factor 1.0, they will be scaled so that they occupy the space which would be occupied by the crystal in the absence of symmetry elements. Similarly, the scaling for the mirror planes and crystal should be reduced with respect to this original scaling - factors of about 0.7 and 0.6 respectively are reasonable. In the Fixed scaling mode the scale factors specified in the Scaling dialog apply to the crystal, and the factors for symmetry axes and planes are scaled relative to the crystal.
The Symbol size determines the maximum dimension of the symbols drawn on both ends of each symmetry axis. The thickness is twice the cylinder radius for the axes (above).
There is a sample of each crystallographic symmetry group or crystal class in the \GROUPS subfolder or directory.
When in the Cartesian or QSHAPE mode (not supported in the Standard Edition), information on the symmetry operators must be present in the .SYM file (Cartesian Symmetry). This information follows the actual symmetry matrices in the form of lines beginning with the keyword SYMOP. This is followed by three floating-point values giving the orientation of the symmety element in Cartesian coordinates, and an integer giving the order of the symmetry element. An inversion axis is denoted by a negative sign. A mirror plane is denoted by order -2, and the coordinates are for the perpendicular to the plane.
Only one symmetry operator of each independent set should be given - the rest are generated by the symmetry matrices. In many cases these operators are just those which are required to generate the symmetry group in the program SYMGRP, and SYMGRP will now write out the generating operators as SYMOP lines. However, in some cases additional sets of operators are generated. SYMGRP will add a mirror plane perpendicular to any rotation axis of even order if a center of inversion is present, but there are still some cases in which operators may have to be added manually. For example, the non-centric icosahedral group I can be generated with only one three-fold axis and one five-fold axis (actually, only one operation of each), but a set of 2-fold axes is implicit in the group and must be added.
See the .SYM files in the \SYM subfolder for examples, which include the icosahedral and pentagonal groups.
Note that some trigonal, tetragonal and hexagonal point groups may have alternate orientations of the symmetry elements with respect to the crystallographic axes - see Symmetry.