Page 73 - Materials Chemistry, Second Edition

60 2 Solid-State Chemistry

One way to visualize the 32 crystallographic point groups is to use stereographic
projections (Figure 2.37). The symbolism used to illustrate rotation axes are as follows:
Twofold (diad):
Threefold (triad): ~
Fourfold (tetrad):
Sixfold (hexad):
Mirror planes are indicated as solid lines, and may be positioned perpendicular or
parallel to the plane of the paper.
As illustrated by the stereographic projections in Figure 2.37, the 6mm crystallo-
graphic point group is observed to have a primary sixfold axis of rotation, with two

Figure 2.37. Stereographic projections illustrating both general positions and symmetry operations for
the 32 crystallographic point groups. Shaded and open circles indicate a general position on the front and
back hemispheres, respectively.