A combination of the point group symmetry operations leads to 32 point groups . As they can be deduced from the macroscopic crystal symmetry, they are also referred to as the 32 Crystal Classes . For the same reason, the symmetry elements that give rise to the Crystal Classes are sometimes referred to as external symmetry elements. Crystal Systems and Bravais Lattices Let us now consider in which way we can translate our cell contents in 3 dimensions to obtain a crystal. The translations which are allowed create 14 Bravais lattices which belong to 7 crystal systems .
Screw axes are very common in protein structures.
Clearly, this is not a point group operation. We will discuss this shortly. One also cannot distinguish a rotation axis from a corresponding screw axis or a glide plane from a mirror plane by just looking at the crystal faces. Currently none of the AF microscopes are good enough to see this. The International Tables list those by symbol and number, together with symmetry operators, origins, reflection conditions, and space group projection diagrams.