CHAPTER III 

 ISOMETRIC SYSTEM 



THE 32 TYPES OF CRYSTALS 



( 'UYSTAL forms, from a consideration of their symmetry alone, 

 are grouped into 32 types ; when referred to their axes, they fall 

 into six systems. The types which are included in any one system 

 are independent, and one type cannot combine with another to 

 form crystals even though they belong to the same system ; each 

 type possesses a symmetry entirely its own, a characteristic derived 

 from the molecular arrangement and molecule itself. At the same 

 time all those included in one system are related by the possession of 

 axes or planes of symmetry to a large extent common to the group. 

 For this reason the old classification of holohedrons, hemihedrons, 

 etc., is also given, and their derivation one from the other, as the 

 best method for the beginner to obtain a clear understanding of the 

 relation of types and the influence of planes and axes of symmetry 

 in the development of crystal forms. 



Under the isometric system are grouped all those crystal forms 

 which are referred to three equal interchangeable axes, intersecting 

 at 90. It includes five types, all of which are characterized by at 

 least four trigonal and three digonal axes of symmetry. Since the 

 crystallographical axes are all equal, they are designated by the 

 symbol a, and a becomes the unit of measurement on these axes. 

 The most general set of parameters is therefore na : a : ma, in which 

 the two variables n and m may have any value between unity, 

 when the plane intersects that axis at unit length or a, and infinity, 

 when the plane is parallel to that axis, or intersects it at infinity. 

 From this standpoint all forms in the system may be considered 

 as special cases of the most general form. 



CLASS, ISOMETRIC HOLOHEDRAL, HOLOSYMMETRIC, OR NORMAL 

 TYPE 32, DITESSERAL CENTRAL 



This type possesses the highest symmetry possible in any crys- 

 tal form, and, as in all holohedral classes, the forms are bounded by 



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