CLEAVAGE. 



Fig. 89. 





Fig. 89 exhibits this tetrahedron separately, its 

 planes being marked with the same letters as appear 

 on the planes of the octahedron, fig. 84, which are 

 parallel to those of the included tetrahedron. 



* 



* 





The tetrahedron thus obtained may be regarded as 

 an imperfect octahedron, four of its planes being con- 

 cealed, or covered by smaller tetrahedrons, p q r s, 

 p q u t, u q x T, q x r #, as in fig. 90, and it is 

 capable of being reduced again to the perfect octa- 

 hedron by the removal of those masses of cubic 

 molecules which constitute the tetrahedrons by which 

 the concealed planes are covered. 



The tetrahedron and octahedron have thus ob- 

 viously the same set of cleavages, and if the tetra- 

 hedron be the primary form, the octahedron may be 

 regarded as an imperfect tetrahedron, requiring cer- 

 tain additions to complete that form.* 



* The student is advised to trace the relation of the octahedron to 

 the acute rhomboid and tetrahedron, by means of an octahedron of 

 fluor produced by cleavage or otherwise. Let him place this on a 

 table, and by the assistance of a small hammer and a knife, he may 

 procure from it, by well observing the figures as he proceeds, the 

 acute rhomboid, a#d tetrahedron, and from them he may re-produce 

 the octahedron. 



