138 



mn. Again, a, b, and c, when revolved around mn as an axis 

 180, will become congruent with x, y, and z. The molecules a, 

 b, c are said to occupy a twinning position in regard to x, y, z, and 

 the two individuals are said to be twins. The axis of revolution 

 b c is the twinning axis, and a 



plane at right angles to the 

 twinning axis is the twin- 

 ning plane. The plane 

 separating the two indi- 

 viduals is the composition 

 or contact plane ; this with 

 rare exceptions is parallel to 

 a possible crystal face. 



The twinning axis is either 

 parallel to a possible crystal 



edge or perpendicular to a possible face. It can never be an axis of 

 even symmetry, as by a revolution of 180 around such an axis the 

 two individuals would be congruent and form a simple crystal. 

 Fig. 276 represents a simple crystal of gypsum ; Fig. 277 is a twin 



FIG. 276. Gypsum Crystal showing the Position of the Twinning Plane. 



crystal of gypsum in which the twinning axis is parallel to the 

 vertical axis c. Fig. 278 is a twinned crystal of gypsum in which 

 it may be seen that one individual has been revolved around the 



