operations for space groups, and the alternative Hermann-Mauguin notation was
more widely adopted and published by the International Union of Crystallography. It
proved to be an essential source book for crystallographers and was invaluable for
the early crystallographic structural investigations when computers and the ability to
access websites were not available. Model building and optical techniques were used
to unravel the patterns observed in diffraction patterns, and these were greatly
assisted by these symmetry considerations.
Trigonal
Hexagonal
Cubic
Tetragonal
Orthorhombic
Monoclinic Triclinic
Primitive
Face centred
Body centred
Fig. 4 The 14 three-dimensional Bravais lattices. For the face-centred and body-centred lattices,
the additional atom lattice sites are shown in colour although all lattice points are equivalent
7 Crystal systems
14 Bravais Lattices
230 space groups
32 point groups
Add rotation, reflection
and inversion symmetry
operations
Introduce face and
body centering
Add screw and
glide symmetry
operations
Fig. 5 The relationship between the 7 crystal systems, the 14 Bravais lattices, the 32 crystal point
groups and the 230 space groups
Early History of X-Ray Crystallography
13