II) 



NEW YORK STATE MUSEUM 



Fig. 21 



A crystal is symmetric to an axis of tetragonal symmetry 

 when it occupies the same position in space four times during 

 one revolution about the axis, the coinciding positions being 90° 

 apart. Fig. 17 and 18 show a crystal of zircon, c-c being an 

 axis of tetragonal symmetry indicated by the sign^. 



Hexagonal symmetry is shown when a 

 crystal occupies the same position in space 

 six times during one complete revolution 

 about the axis of symmetry, the coinciding 

 positions being 60° apart. Fig. 19 and 20 

 show a crystal of quartz, c-c being an axis 

 of hexagonal symmetry indicated by the 

 sign 4f^. 



A crystal is symmetric to a point or center 

 when every imaginary straight line passing- 

 through that point intersects the crystal at its two extremities 

 in similar faces, edges or solid angles. This is the least sym- 

 metric of all the conditions so far discussed and is illustrated 

 by the crystal of chalcanthite or blue vitriol shown in fig. 21. 



Crystallographic axes 



The relations between the faces of a crystal are best studied 

 by assuming certain directions within the crystal called axes. 

 Such axes may, in the more symmetric groups, be axes of sym- 

 metry, and when the crystal is symmetric to one or more 

 planes of symmetry, they bear a definite relation to those 

 planes. 1 Three (in one system four) such axes are chosen, their 

 relative inclination and lengths forming a basis for classifying 

 all crystals into six systems. 



If the symmetry of a crystal permits the grouping of faces 

 around one axis to be identical with the grouping of faces 

 around another, the two axes are said to be interchangeable. 

 In fig. 17 and 18 the axes marked a are interchangeable but 



1 In the normal groups of the isometric, tetragonal, hexagonal and ortho- 

 rhombic systems, the axes are found at the intersection of the planes of 

 symmetry, and in the normal group of the monoclinic system two axes lie 

 in the plane of symmetry and a third is perpendicular to it. 



