hy Means of Grajphical Methods. 



26" 



The trisoctahedrori bevels the edges of an octahedron ; its 

 poles, therefore, are always to be found on the zones between 

 octahedron and dodecahedron. Taking a crystal of galena, an 

 octahedron with bevelled edges, as an example, the angle of 

 the trisoctahedron, measured over an octahedral edge, is 38° 56^ 

 One-half of the foregoing angle, 19° 28^, is therefore that of 

 trisoctahedron on dodecahedron, and the pole between 110 and 

 111 is easily located by means of the stereographic scale. To 

 determine the symbol of the form, which, being in the zone 

 between 110 and 111, must have a 1 : 1 relation on the first 



16 



01 0' 



ioo 



i^Toia 



and second axes, draw the line from 010 to 100 and thns de- 

 termine the base-line Oy. The slope of the face, its angle on 

 001, is 70° 32' (complement of 19° 28'), hence from y (the 

 base-line transposed to the horizontal diameter) construct a line 

 at T0° 32', which, if continued, will meet the vertical axis 

 (radius) at 2a. The form intersects the axes, therefore, at 

 a \ a \ 2«, the indices being 221. To fix the pole 212 between 

 111 and 101, place the small circle protractor over the projec- 

 tion, its zero at 010, and space off the distance 19° 28' from 

 101 with dividers ; then transpose to the paper. Another and 

 better way is to lay ofl: the distance 19° 28' from 001 on the 

 horizontal diameter, and construct a small circle with radius 



