Symmetries of 3D crystals

The relations between the cell sides (a, b, c) and cell angles (a, y) are shown and the corresponding lattices are labeled P = primitive, I = body-centerei C = side-centered, F = face-centered, R = rhombohedral. 

System Cell sides Cell angles Lattices Point groups 

A number of possible point groups are associated with each of the 14 Bravais lattices, depending on the symmetry of the basis. There are 32 point groups in all, denoted by the following names  

D for dihedral , when there are two-fold axes at right angles to another axis  

T for tetrahedral , when there are four sets of rotation axes of three-fold symmetry, as in a tetrahedron (see Fig. 3.11)  

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