86 



MINERALOGY 



lateral crystallographical axes. The remaining three bisect the 

 angles between the lateral axes. There are seven planes of sym- 

 metry, one of which, the equatorial plane, contains the didigonal 

 axes and is at right angles to the c axis. The other six planes all 

 intersect in the c axis and each contains one of the didigonal axes. 

 They are therefore inclined to each other at an angle of 30, Fig. 151. 

 These seven planes of symmetry divide space into 24 equal por- 

 tions or solid angles. The largest number of faces on any hexag- 

 onal form will be 24, or one face in each solid angle. There is 

 also a center of symmetry and the forms of this type will all be 

 bounded by pairs of parallel faces, Fig. 152. 



Forms 



I. Dihexagonal pyramid ; na 



n 



n i 



a : a : me 



(hkil). 



This form is represented by one face in each of the 24 solid angles 

 and is bounded by 24 scalene triangular faces, Fig. 153 ; each face 



FIG. 153. Dihexagonal Pyramid, 

 na : - a: a: me; (hkil). 



FIG. 154. Hexagonal Pyra- 

 mid of the First Order, 

 a : ooa : a : c, (hohl). 



cuts the lateral axes at a different distance. The equatorial edges 

 are all equal, and the alternate polar edges are equal. 



II. Hexagonal pyramid of the first order ; a : oo a : a : me ; (hohl). 



If the poles in Fig. 152 be moved into the intermediate planes 

 of symmetry so as to lie on that side of the triangle between the 

 intermediate and the hexagonal axes, then the number of faces will 

 be reduced to 12, and a new form will result, the hexagonal pyra- 

 mid of the first order, Fig. 154, bounded by 12 isosceles triangles. 



