J. C. KENDREW and M. F. PERUTZ 



of different length), rhombohedral (three equal axes, angles all equal 

 but not 90°), tetragonal (two axes equal and different from the third, 

 all angles 90°) to cubic (three equal axes at right angles). 





Figure 1. Patterned wall- 

 paper. ' Unit cells ' are indi- 

 cated bv lines. 



Each unit cell may contain one, two, or more molecules, oriented at 

 various angles to one another. The contents of the cell nearly always 

 exhibit certain symmetry properties. For example, it may be possible 

 to draw through the cell a plane such that one half of the cell is the 

 mirror image of the other half (mirror plane) ; or a line such that any 

 piece of matter in the cell if rotated through 180° about the line comes 

 into exact coincidence with an identical piece of matter (diad axis of 

 rotation) ; or an axis such that rotation through 90° produces coin- 

 cidence (tetrad axis). Other symmetry properties may be exhibited, 

 and mathematical analysis has shown that in three dimensions the 

 possible combinations of symmetry elements yield in all 230 distinct 

 space groups. 



Although the unit cell is strictly the smallest repeating unit of 

 pattern, the existence of symmetry elements implies that within the 

 cell there are generally still smaller units, identical but in different 

 orientations. (In Figure 1 the unit cell of the wallpaper contains two 

 identical units, related by a mirror plane.) The smallest such unit has 

 the property that, if the symmetry elements be allowed to operate upon 

 it (if, for example, it is reflected in any mirror planes, and both it and 

 the reflexions are rotated round axes of rotation, etc), the whole 

 contents of the cell are produced. This unit, which may consist of a 

 single complete molecule, or of part of one molecule and part of 

 another, or of part of one molecule only (where the molecule is built 

 up of identical sub-units), is known as the asymmetric unit. Its size can 

 at once be determined if the unit cell dimensions and space group {i.e. 

 symmetry properties) are known. 



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