376 



C. K. SAYARTZ PROPOSED CLASSIFICATION OF CRYSTALS 



b. No singular axis is present. Three equal axes with periods of 

 2 or 4. 



Crystals of this class are doubly terminated, the faces of the 

 upper pyramid being directly over those of the lower. Its sym- 

 metry may be derived from that of the Hedral class by passing 

 a plane of symmetry normal to the planes of symmetry of that 

 type. It is hence named Orthohedral (orthos = perpendicular. 

 hedra = a plane). 

 6. Planes alternating with the axes — Amebahedral class (figure 12). 



Vertical planes of symmetry may be passed between the lateral 

 axes with which they then alternate, developing an alternating 

 axis at their intersection. Since the smallest number of lateral 

 axes is two, alternating with two planes, the lowest possible 

 period is 4. Having many axes, two possibilities are presented : 



a. A singular axis is present with periods of 4 or 6. 



Figure 11.— Orthohedral 



class. 



Figcbe 12. — Aniebahedral 



class. 



Figcek 13.— Aruebaxial 

 class. 



Figuek 14.— Three-fold alter- 

 nating axis producing orthohe- 

 dral svmmetrv. 



ft. No singular axis present. Three equal axes occur with periods of 4. 



These crystals possess alternating vertical planes and horizontal 

 lateral axes of symmetry, while their faces alternate about the 

 vertical axis. They are hence termed Amebahedral (amoWos = 

 alternate, hedra = a plane). 



This manifestly exhausts all possible types of symmetry due to 

 reflection about planes. 



III. Symmetry by combined rotation and reflection. In addition to 

 the preceding, it is possible to combine rotation and reflection simul- 

 taneously in one act, producing a third type of symmetry. This is the 

 combined (zusammengesetzte) symmetry of Fedorow. A single class de- 

 velops here. 



7. Amebaxial class (figure 13). 



These crystals are without ordinary axes or planes of sym- 

 metry, but possess a single axis of alternating symmetry. This 

 fact may also be expressed by stating that they have a combined 

 axis and plane of symmetry normal to it, or. more simply, that 

 they have a single axis of alternating symmetry. 



This axis can have periods of 2, 4, G only. A three-fold alter- 

 nating axis is impossible. If assumed, it will produce faces which 

 are directly over each other — that is. they will not be alternating. 

 (See projection, figure 14.) 



