ISOMKTKU SYSTEM 



itv, hence the term polar. The 

 (ry-tallographic a\<- are didigonal 

 The six planes of sym- 

 metry I >iaect the octants :u id pa-> 

 through opposite edges of the cube, 

 l-'ifT. 89. 



Symmetry, 4 ditrigonal polar 

 axes, H didigonal axes, and (1 

 piano. There being no center of 

 symmetry, the forms are not 

 bounded by parallel faces. 



Fia. 89. Diagram of Axes and 

 Planes of Symmetry in Type 31. 



Forms 



I. Hextetrahedron ; 



na : a : ma 



(hkl) K (hkl). 



In grouping the faces around the isometric axes so as to conform 

 to the symmetry of any type, it is necessary to cut all extremities 

 of the rrvstallographical axes with the same number of faces 

 and at the same inclination, since the axes are interchangeable. 

 If planes are grouped on the axes, fulfilling the symmetry of this 

 type, the most general form will be bounded by 24 similar scalene 

 triangles, Fig. 90; six faces are grouped around the ditrigonal, 



FIG. 90. The Hextetrahedron, 

 K (hkl). 



FIG. 91. The Hextetrahedron, 



K(hkl). 



four around the didigonal axes. The spherical projection, Fig. 

 91, shows that the poles (circles) in the northern hemisphere do not 

 reflect those in the southern hemisphere (crosses) ; therefore the 

 plane of projection is not a plane of symmetry. If this projection 

 is compared with Fig. 73 a, it will be seen that the poles of the hextet- 



