90 



MINERALOGY. 



Again, if the student cut off the corners of the solid angles 

 of the octohedron (fig. 22), and continue to enlarge these 

 planes equally till the faces of the octohedron disappear, a 

 cube will be formed. 



Or, if the twelve edges of the octohedron be replaced by 

 tangent planes (fig. 23), 



FIG. 23. 



FIG. 24. 



FIG. 26. 



and if these be continued till they intersect, the rhombic 

 dodecahedron will be the result (fig. 24). 



By the replacement of the four alternate solid angles, or 

 corners of the cube, till the cubic faces disappear, the tetra- 

 hedron may be formed ; and by replacing 

 all the edges of the cube with tangent 

 planes till they intersect, the rhombic 

 dodecahedron, fig. 24, may be produced. 



In speaking of the replacement, or cut- 

 ting off the edges, or solid angles, we do 

 not, of course, mean that these have actu- 

 ally been cut off; for, in fact, they never 

 existed ; but what is meant is, that the same 

 appearances are produced, as if such truncations had actually 

 taken place. 



"We have recommended the pupil to preserve the slices 

 which he has taken, off, in producing the cube from the 

 octohedron, and the octohedron from the cube, because 

 each of these forms being deducible from the other, he will 

 only have to replace them to form the cube on the octohedron 

 by addition, as the octohedron was formed from the cube by 

 diminution ; and again, after reducing the octohedron to the 

 cube, he may form the octohedron on the cube by restoring 

 the slices he has removed. 



The secondary forms of crystals are supposed to have 

 arisen, from the regular arrangement, on the planes of the 



