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 an 
30. al. 32. 
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octahedron and a trigonal trisoctahedron, fig. 34 ; fig. 35, a form 
between a dodecahedron (planes 7) 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 
of figures.—The numbers by which the planes in the above figures, 
and others of the work, are lettered, indicate the positions of the planes 
with reference to the axes, and exhibit the mathematicai symmetry 
and 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 @; that meeting the side plane to the 
right 6, and the vertical axis c, and the other halves of the same axes 
respectively -a, -b, -c. By astuly of the positions of the planes of the 
