PRINCIPLES OF CRYSTALLOGRAPHY. 



151 



Fig.rAb 



plane ; it is to be determined if symmetry with regard to another plane 



does not follow from it ; given a zone, which is symmetrical with respect 



to one or more faces, i. e., that for every 



face of the zone there is also a possible 



one which will be symmetrical with it^ 



it is required if from this, symmetry in 



other directions does not follow, i. e., 



if for ever}' i^ossible face of the given 



zone another face is not also possible, 



with which, according to presumption, 



the zone sought for is parallel. 



The criterion of the possibility of a face is, therefore, always the ra- 

 tionality of its indices. Proceeding in this way, we recognize that only 

 that reunion of faces is, crystallographically speaking, possible, which, 

 by the number and position of their planes of symmetry, belong to one 

 of the seven characteristic crystalline systems. By plane of symmetry 

 of a crystal we understand a plane in relation to which all the possible 

 faces of a crystal are symmetrical, so that for every possible face of a 

 crystal there is another which, so far as the plane of symmetry is con- 



Fig.l^. 



Fig. 16 



cerned, is symmetrical with it. It is therefore apparent, that only the 

 following combinations are possible: 



1. '^0 plane of symmetry existing Triclinic system. 



2. One plane of symmetry, B, (Fig. 14) Monoolinic system. 



3. Three difierent planes of symmetry at right angles to each other, 



A, B, C, (Fig. 15) Ehombic (orthorhobibic) system. 



4. Three tautozonal and simdar planes of symmetry inclined to each at 

 angles of 60° and 120°, A A' A", (Fig. 16), Ehombohedral system. 



