Crystal symmetries stereographic projections

All thirty-two crystal classes in stereographic projection are tabulated in Fig. 9.1.8. For each crystal class, two diagrams showing the equipoints and symmetry elements are displayed side by side. Note that the thicker lines indicate mirror planes, and the meaning of the graphic symbols of the symmetry elements are given in Table 9.3.2. 

Symmetry elements and stereographic projection of crystal class 43m. 

Morphology Measure the angles between crystal faces if they are well developed. Drawing a stereographic projection (see Chapter 2) may help. Note any cleavage directions and any tendency to form twins. Sometimes etching of the crystal faces will reveal their symmetry. 

Although the word crystal in its everyday usage is almost synonymous with symmetry, there are severe restrictions on crystal symmetry. While there are no restrictions in principle on the number of symmetry classes of molecules, this is not so for crystals. AH crystals, as regards their form, belong to one or another of only 32 symmetry classes. They are also called the 32 crystal point groups. Figures 9-12 and 9-13 illustrate them by examples of actual minerals and by stereographic projections with symmetry elements, respectively. 

Fig. 2.20. Stereographic projections of the symmetry elements and the equivalent positions for the 32 crystal classes...

The last idea is crucial the purpose of introducing the spherical and stereographic projection is to systematize in a planar representation the relations of tri-dimensional symmetry existing between the planes (associated to the faces) and between the important directions into a crystal. 

Depending on the orientation of the electric field propagation direction, e g. respecting the symmetry directions in the crystal belonging to the 42m point group, with the stereographic projection 19 of Table 2.8, - the crystal under concern, under electric field, will perceive one of the symmetries resulted in Figure 2.57, as based on the application of the relation (2.99). 

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