464 On C'-ystattography. 



\ What has been said relative to the parallelopipedon is of 



^ itself appHcablcto the other primitive forms. We shall gO 

 over them successively. 



Fig. 64. represents the expression of the octahedron with 

 scalene triangles ; fig. 60. that of theoctahedron with isosceles 

 triangles, and lig. ti(). that of the regular octahedron. 



In order to place the cyphers which accompany the letters, 

 we shall conform to what has been said relative to the 

 rhomboid. Thus in fig. 05. we shall place the cypher below, 

 for the dccrenjents which set out from the angle A or from 

 the ridge B ; above, for those which set out from the ridge D j 

 and on one side for those which set out from the angle E. 



Ff we wished to designate the result of a decrement by 

 one range on all the angles of the regular octahedron 

 (fig. QQ.)y ^c should write A 'A' ; and in order to indicate 

 the result of a decrement by one range on all the edges, we 

 should write BB. The first of these decrements produces 



a cube, and the secohd a dodecahedron with rhombic planes. 



In some species, such as nitrated potash, the primitive oc- 

 tahedron, the surface of which is composed of eight isoscele 

 triangles four and four similar to each other, ought to have 

 the position represented in fig. 67-, in order that the secon- 

 dary crystals may be in the most natural attitude, i. e. that 

 theVidgcs at the junction of the two pyramids which com- 

 pose the octahedron Ought to be partly in the vertical di- 

 rection like F, and partly in the horizontal direction like B. 

 On comparing fig. 67. with fig. 68., in which we have acted 

 by placing the letters as if all the angles and all the ridges 

 had particular functions, we shall easily conceive the distri- 

 bution adopted in fig. 67., and reduced to the symmetry of 

 the true prmiitive form : for in the present case we have 

 E=A,D = C, G = F. 



We shall place the index cypher below the letter, with 

 respect to decrements which set out from B ; on one side 

 or below with respect to such as set out from A, according 

 as their eflect shall be referred to the triangle A I A or to 

 the triangle A I V ; above or below with respect to those 

 which set out from C, according as their effect shall take 

 place in the same way on the first or on the second triangle; 

 on one side with respect to the decrements which set out 

 from F; above and below, or on both sides, for the decre- 

 ments which set out from I, according as their efiect shall 

 be directed towards B or towards F. 



The tetrahedron being always regular, when it becomes 

 the primitive form, its expression will be represented fig. Cg. 



llL 



