50 



MINERALOGY 



III. Tetragonal Trisoctahedron ; na:a:na; (hhl), Fig. 76. 



If in place of moving the pole of the most general form (hkl) 

 to the diametral plane, it be now moved into the planes of symmetry 

 which bisect the octants, and between the ditetragonal and ditrig- 

 onal axes ; as the poles approach the plane the angle between the 



FIG. 76. The Tetragonal Trisocta- 

 hedron, (hhl). 



FIG. 77. The Tetragonal Tris- 

 octahedron. 



normals constantly diminish until the plane is reached, when it 

 becomes 0, Fig. 73 a, and the angle between the faces they represent 

 is 180. Thus two faces, b and c, a and e, of the most general form 

 will coalesce, producing a form bounded by 24 four-sided faces, 

 Fig. 76, having three faces entirely within each octant. Four 

 faces are grouped around the ditetragonal, three around the ditrig- 

 onal, and four around the didigonal axes. In this form, also, the 

 solid angles between faces will vary with the value of n, yielding a 

 series. The tetragonal trisoctahedron may be produced by re- 

 placing each face of the octahedron with three tetragonal faces. 



IV. Trigonal Trisoctahedron; a: a: na; (hhi), Fig. 78. 



Let the poles of the most general form now be moved till they lie 

 in the plane of symmetry between the ditrigonal and didigonal 

 axes, Fig. 73 a. Again two faces, a and b, a' and b', of the most 

 general form will fall in one plane, producing still a third form 

 bounded by 24 faces, Fig. 78 ; each face is an isosceles triangle with 

 its base lying in the diametral plane. Eight of its faces, Fig. 79, are 

 grouped around the ditetragonal, three around the ditrigonal, and 

 the didigonal axes bisect the base of the triangular face. As in 

 the preceding forms the solid angles vary with the value of n, 

 producing a series of trigonal trisoctahedra. 



