66 



MINERALOGY 



planes of symmetry) Fig. Ill, one of which is the equatorial plane; 

 the other four intersect in the c axis and each contains one of the 

 axes of symmetry lying in the- equatorial plane. The five planes 

 divide space into 16 equal (Fig. 112) triangular portions, eight 

 above and eight below the equator. The largest number of faces 

 possible upon any form of the tetragonal system will be 16. 



Forms 



I. Ditetragonal pyramid ; na:a:mc; (hkl). 

 When the values of n and m are between their limits, the pole 

 of the face will fall within the area of the triangle, Fig. 112 ; there 

 will be one face in each triangular space, yield- 

 ing a form, the ditetragonal pyramid, Fig. 113, 

 bounded by 16 scalene triangles (pyramid here 

 includes the faces above and below the equator 

 and are doubly pointed). It has eight faces 

 grouped around the north and eight around the 

 south pole or c axis ; four faces grouped around 

 the extremities of the didigonal axes. There is 

 a series of ditetragonal pyramids, the shape of 

 the face or the value of the interfacial angles of 

 any one of which will depend upon the values 

 of n and m. 



II. Tetragonal pyramid of the first order; 

 FIG. us. The Ditet- a : a : me ; (hhl). 



When the value of n is unity, its minimum 



ragonal Pyramid. 



limit, or if the pole in the spherical projection, Fig. 112, is moved 

 until it coincides with the intermediate axes, then two adjacent 

 poles of the most gen- 

 eral form, as a and c, 

 will combine, yielding a 

 form bounded by eight 

 isosceles triangles, Fig. 

 114, the tetragonal pyr- 

 amid of the first order. 

 Its eight polar edges 

 are equal. The crystal- 

 lographical axes termi- 

 nate in a solid tetrahe- 



dral angle; this char- FIG. 114. Pyramid of the First Order (111), of 



acterizes a pyramid of Cassiterite. 



the first order ; in pyramids of the second order the a axes bisect 



