EXERCISES ON CRYSTALLINE FORMS. 109 



EXEECISES 



ON CRYSTALLINE FORMS. 



1. LET the student take a piece of soap, or of cork, and 

 cut it into a form resembling fig. 19, lie will produce a cube, 

 and will thus form the first geometrical figure in the series. 



2. Cut off the corners regularly and evenly, so as to leave 

 a neat little triangle at each corner, he will thus have replaced 

 the solid angles by triangular planes (fig. 20) . 



3. Continue cutting off the corners till 

 the faces of the cube disappear, and he will 

 effect another modification ; the cube will be 

 changed to the octohedron (fig. 21). 



4. Cut off the corners of the octohedron, 

 FIG 57 and you will produce figure (fig. 57). And 



if you continue these cuttings till the faces 

 of the octohedron disappear, a cube will again be formed 

 (fig. 22). 



5. Form a cube a second time, and cut away its four alter- 

 nate corners, till the faces of the cube are destroyed, and you 

 will form a tetrahedron (fig. 32). 



6. Form a cube a third time, and cut off its edges evenly 

 and neatly, so as to take off as much on one side as the other, 

 you will have replaced the edges of a cube by tangent planes, 

 as figs. 16 and 32. 



7. Continue these cuttings till they intersect, and the 

 rhombic dodecahedron will again be produced (fig. 34). 



8. Form an octohedron, and cut off its twelve edges in a 

 like even manner, and you will likewise replace its edges by 

 tangent planes (fig. 17). 



9. Continue these cuttings till they touch each other, and 

 you will again produce the rhombic dodecahedron (fig. 34). 



10. Form a cube for the following purpose. Cut off the 

 corners very carefully and regularly, and as carefully lay the 

 slices aside till you have formed the octohedron. Then 



