DEVELOPMENT OF GROUPS AND CLASSES 375 



These crystals are doubly terminated, producing right- and left- 

 handed forms which are enantiomorphous, and all manifest circu- 

 lar polarization. They are termed Poly axial (polus = many, 

 axon = an axis). 

 II. Symmetry by reflection about planes. The second fundamental 

 type is symmetry by reflection. 



Method of development. — It has already been shown that when planes 

 of symmetry intersect they produce an axis of symmetry at their intersec- 

 tion. It is therefore necessary that the axes so formed should be iden- 

 tical with those already discussed. The simplest way of developing these 

 classes, therefore, is to take the preceding axis and pass planes of sym- 

 metry through them, employing first one axis, then many axes. 



A.. One axis. — Planes may be passed through one axis in two positions. 



3. Plane normal to the axis — Orthoaocial class (figure 8). 



The axis may possess the periods 2, 3, 4, 6, giving rise to four 

 groups. These crystals are doubly terminated, the upper faces 

 being directly over the lower while the plane is normal to the axis. 

 The class is hence termed Orthoaxial ( orthos = perpendicular, and 

 axon = an axis). 



A plane of symmetry can not pass obliquely to a single axis, 

 otherwise the axis would be doubled by reflection, as shown in 

 figure 9, where the axis 8 8 is reflected to position 8' S' — that is, 

 the crystals would no longer possess a single axis. One other pos- 

 sibility, therefore, remains. 



4. Planes parallel to the axis — Hedral class* (figure 10). 



Planes of symmetry are passed parallel to the axis which is pro- 

 duced by their intersection, its period equaling the number of in- 

 tersecting planes. 



These crystals are singly terminated and have their faces in 

 pairs in the general form (mPn). They possess planes of sym- 

 metry intersecting in one axis. The class is termed Hedral 

 (hedra = a. plane), since the axis is but the result of the intersec- 

 tion of the planes. 



B. Many axes. — We may now pass planes through many axes. Planes 

 may be passed through them in two positions only, either coinciding with 

 the axes or alternating with the axes. 



5. Planes coinciding with the axes — Orthohedral class^ (figure 11). 



Here the planes pass through the axes which are formed at their 

 intersections. Having many axes, two possible cases present 

 themselves : 

 a. A singular axis is present with periods of 2, 3, 4, 6. 



* This class may also be termed Monaxihedral (having planes intersecting in one 

 axis) or, for simplicity, Monohedral (singly terminated pyramids of the hedral type). 

 t This class may also he termed Polyhedral ; that is, having many planes of symmetry. 



