. 88 



Fig. 91. 



hedron {111} is eventually split up into a positive and a negative 



tetrahedron. 



Besides the general 

 forms {hkl} , in the 

 uy.&nAyvurf- ^.^t^cf^f fig. Q2 , the whole series 

 of simple forms which 

 occur for determined 

 values of h and k, are 

 reproduced here; the 

 crystals in nature are 

 of course generally 

 more or less complica- 

 ted combinations of 

 several of these simple 

 forms occurring at the 

 same time, and usually 

 with very different relative development of the existent forms. 



That gradual trans- 

 itions between these 

 forms can be imagi- 

 ned with variation of 

 the values oih,k, and 

 / from zero to every 



arbitrary integer 

 number, is obvious 

 on " comparing the 

 different simple forms 

 with each other. 



In this way we have 

 made clear the general 

 method of description 

 of crystallographical 

 polyhedra, and their 

 definition with res- 

 pect to their sym- 

 metry-properties. By Fi 92 

 the application of this 



principle to the other possible classes, we shall arrive at all 

 possible simple forms of crystals, and thus the consequent develop- 

 ment of these ideas is best left to treatises on crystallography, as 



