FUNDAMENTAL FORMS OF CRYSTALS. 



29 



By means of such models, the student may trace out im* 

 portant relations between the fundamental forms. 



Take a cube, and cut off each angle evenly, inclining the 

 knife alike to the adjacent faces ; this produces figure 20. 

 Continue taking slice after slice equally from each angle, 

 and the solid takes the form in fig. 20a, (called a cubo-octahe- 

 dron ;) still continue taking off regular slices from each angle 

 alike, and it finally comes out a regular octahedron, the form 

 represented in fig. 20b. The last diminishing point in each 

 20 20a 20& 



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face of the cube is the apex of each solid angle of the octa- 

 hedron. It is hence apparent why the axes of the cube con 

 nect the opposite solid angles of the octahedron. 



Take another cube (one of large size is preferable) and 



pursue the same process with each of the edges, keeping the 



knife, in cutting, equally inclined to the faces of the cube, 



and we obtain, in succession, the forms represented in figs. 



21 21a 216 



21 and 21a ; and finally as the plane P disappears, it comes 

 out the rhombic dodecahedron, (fig. 21 b.) Hence the same 

 axes which connect the centers of opposite faces in the cube, 

 connect opposite acute solid angles in the dodecahedron. 



So the cube, by reversing the process, may be made from 

 an octahedron by cutting off its solid angles, passing in suc- 

 cession through the forms represented in figures 20Z>, 20a, 

 20, to figure 1. The dodecahedron also yields a cube in a 

 similar manner, giving as the process goes on, the forms rep- 

 resented in figures 2\b, 21a, 21, 1. 



Moreover, the octahedron and dodecahedron are easily de- 



How can you make an octahedron from a cube ? How make a do 

 decahedron from a cube? How the cube from an octahedron? th<> 

 cube from a dodecahedron ? What relation hence exists between the 

 solids of the first syptem ? 



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