132 R. W. G, Wyckoff— Theory of Space Groups 



at the space groups and at the structure of crystals. A 

 crystal, or the space grouping, may be divided into units 

 of structure, unit parallelopipeds, which are all alike and 

 similarly oriented, by planes passing through the prin- 

 cipal directions of symmetry {f^g. 2) parallel to the axes 

 of coordinates. Thus, if the crystal is monoclinic, it 

 would be divisible into monoclinic prisms ; if it is cubic, 

 the units are cubes, and so on. The planes bounding 

 these units pass through points of the lattice and the 



Fig. 3. —A portion from a space lattice. The black circles represent points 

 of the lattice. OA, OB. and OC are translations of + 2 t^. + 2rv, and + 2tz 

 respectively. OADBGCFE is the unit prism. 



resulting unit will contain anywhere from one to four 

 "crystal molecules" depending upon the nature of the 

 lattice. In figure 3 the monoclinic prism OAFCGBDE 

 is a unit of structure of the space group C^h^ The 

 eight points of the lattice at the eight corners of the unit 

 prism together contrive to place within it a single crystal 

 molecule.^ ^ 



" This statement may be more readily seen on considering the following. 

 If an atom of the crystal molecule which surrounds O (figure 3) lies inside 

 of the unit it is impossible that the corresponding point of any other crystal 

 molecule of the lattice can lie within this prism. Also the crystal molecules 

 lying about the other seven corners of the unit will furnish within the unit 

 the points corresponding to thoce about O which lie outside of the unit. 

 Thus one crystal molecule is contained within the unit of structure. 



