. 146. OF COMBINATIONS. 173 



. 146. DI-RHOMBOHEDRAL COMBINATIONS. 



A combination of the rhombohedral system is 

 said to possess a Di-rhombohedral Character, if one 

 or more of the simple forms contained in it appear 

 at once in both their positions (. 108.). 



The rhombohedrons and the scalene six-sided pyramids 

 are the only forms of this system which may assume two 

 different positions ; for if the position of the other forms is 

 supposed to change, their faces resume the situation they 

 had before, or, properly speaking, another face exactly 

 takes the place of that which just has been removed from it. 



1. Suppose, therefore, in . 145. i., n' to be = n, or the 

 combination, R + n. R -f n. The sign indicates, that 

 the two rhombohedrons are in a transverse position to each 

 other. The combination assumes the aspect of an isosceles 

 six-sided pyramid (. 35.), which is a simple form, and the 

 edges of combination are parallel to those lines, which, in 

 the faces of the single rhombohedrons, join the apices with 

 the centres of the lateral edges. This form is now desig- 

 nated by the name of a Di-rhombohedron, and its crystallo- 

 graphic sign is either as above 11 + n. II + n, or it is 

 2 (R + n). The difference of this form from the isosceles 

 six-sided pyramids consists in the position, and in the rela- 

 tions existing between their axes and horizontal projec- 

 tions. From the di-rhombohedrons the combinations are 

 denominated, in which these forms occur. 



Let the terminal edge of the rhombohedron be = x, that 

 of the di-rhombohedron = C, being the edge of combina- 

 tion ; we obtain the formulae 



cos. x = 3 cos. C -J- 2, 



cos. C = COS ' X - 2 ; 

 3 



which are useful for finding the dimensions of any di-rhom- 

 bohedron from those of its rhombohedron, and vice versa. 

 In . 145. iii. 1., the faces of the isosceles six-sided py- 



