ISOMETRIC SYSTEM. 



21 



Again, fig. 30 is a form between a cube (fig. 16) and a tetra 

 hexahedron, fig. 31 ; fig. 32, a form between an octahedron, fig. 

 24, and a tetrahexahedron, fig. 31 ; fig. 33, a form between aD 



octahedron and a trigonal trisoctahedron, fig. 34 ; fig. 35, a form 

 between a dodecahedron (planes i) and a tetrahexahedron ; fig. 



36, a form between the dodecahedron and a hexoctahedron, 

 fig. 37. 



Fig. 38 represents a cube with planes of both the octahedron 

 and dodecahedron. 



2. Positions of planes with reference to the axes. Lettering 



©f figures. — The numbers by which the planes in the above figures, 

 fend others of the work, are lettered, indicate the positions of the planea 

 *ith reference to the axes, and exhibit the mathematical symmetry 

 &nd ratios in crystallization. In the figure of the cube (fig. 1) the three 

 axes are represented ; the lateral semi-axis which meets the front 

 planes in the figure is lettered a ; that meeting the side plane to the 

 right b, and the vertical axis c, and the other halves of the same axes 

 respectively -«, -5, -c. By a study of the positions of the planes of the 



