Sixfold rotation axis

Sixfold rotation axis with center of symmetry 6 sub 3 screw axis with center of symmetry... 

We mentioned earlier that the true symmetry of the unit cell may not simply be manifested macroscopically upon infinite translation in three dimensions. Buerger has illustrated this with the mineral nepheline, (Na,K)AlSiC>4 (Buerger, 1978). The true symmetry of the nepheline crystal lattice, the symmetry of the unit cell, consists merely of a sixfold rotation axis (class 6) as would be exhibited by a hexagonal prism with nonequivalent halves. That is, there is no mirror plane perpendicular to the rotation axis. However, the absence of this mirror plane is obviously not macroscopically visible in the hexagonal prism form development of nepheline, implying a higher apparent symmetry (6/mmm). 

D6h One sixfold rotation axis, one symmetry plane perpendicular to it, and six symmetry planes which include the sixfold axis. The six planes are grouped in two sets. One set is rotated relative to the other... 

The symmetry of (he snowflake involves this type of mirror-rotation axis. The snowflake obviously has a center of symmetry. The symmetry class m -6 ni contains a center of symmetry at the intersection of the sixfold rotation axis and the perpendicular symmetry plane. In general, for all m-n.rn symmetry classes with n even, the point of intersection of the n-fold rotation axis and the perpendicular symmetry plane is also a center of. symmetry. When n is odd in an m-n m symmetry class, however, there is no center of symmetry present. 

Figure 38. Zone axis convergent beam electron diffraction pattern revealing the presence of a sixfold rotation axis 1168)...

Six mirror planes at 30° to one another intersecting along a sixfold rotation axis A sixfold rotation axis passing at right angles through the intersection of six twofold rotation axes at 30° to one another... 

Note that the space group for the hep structure is PSs/mme. The point group is 6/mmm, but the subscript 3 next to the 6 signifies additional symmetry in the space group in the form of a threefold screw axis parallel to the sixfold rotational axis. Similarly, the c in place of the last m signifies a glide plane parallel to the c-axis. 

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