lli:\.\<i>NAL SVSTI.M 



87 



Kach face cuts t\vo of tin- lateral axes at an equal distance ami i> 

 parallel to the third. Tin- axes therefore end in the tetraheclral 

 uncles, iiuiking it a pyramid of the first 



order. 



III. Hexagonal pyramid of the second 

 order; 2 a : 2 a : a : me ; (hh2hl). 



If the poles in Fig. 152 are moved into 

 the diametral planes, then the faces of 

 the most general form will be reduced to 

 12 isosceles triangles, Fig. 155, each face 

 cutting two of the lateral axes at an 

 equal distance and the third at one half 

 that distance. The a axes will bisect the _ 



FIG. 15o. Pyramid of the 



equatorial edges, making the form a pyra- Sec ond Order, 2 a . 2 a : a : c, 



mid of the second order. 



(hhahl). 



IV. Dihexagonal prism; na: 



n i 



a : a : ooc; (hkio). 



The poles are now moved to the equatorial plane between the axes 

 of symmetry, when the faces will be reduced to 12, all of which are 





N 



!'['.. 156. Dihexagonal Prism, 



a : a : me, (hkio) . 



Fia. 157. Hexagonal Prism of the 

 First Order, a : oo a : a : oo c, (hoEo). 



parallel to the c axis, yielding an open form, Fig. 156, the dihex- 

 agonal prism, alternate edges of which are similar. 



