I80METRH SYSTEM 



I'.i 



angles of the form will vary with the value of m and n, there i> 

 then ton- a series of hexoctahedra, of which 3 a: a: 2 a is one. 



The spherical projection of the 

 hexoctahednm is represented in Fig. 

 73 a. The planes of symmetry are 

 represented by the great circles in 

 which they cut the sphere of projec- 

 tion. The poles of the faces in the 

 northern hemisphere are represented 

 by small circles, those in the south- 

 ern hemisphere by crosses. The 

 cross within the circle indicates that 

 the two hemispheres are mirror 

 images of each other, and the type 

 is equatorial. The points at which the axes of symmetry emerge 

 are indicated by the conventional signs. 



II. Tetrahexahedron ; na : a : oo a ; (hko), Fig. 74. 



This form is a special case of (hkl), where 1 = o ; or each face 

 cuts one axis at oo, one at unity, and one at an intermediate 

 distance. If the poles of (hkl) are moved, so as to lie in the 

 diametral planes, Fig. 73 a, two normals will coincide, as a with a' 



FIG. 73 a. Hexoctahedroii. 



Fio. 74. The Tetrahexahe- 

 -dron (320), of Fluorite. 



FIG. 75. Tetrahexahedron 

 (320). 



or b with b', producing a form bounded by 24 isosceles triangles. 

 Four faces are grouped around the ditetragonal axes, Fig. 75, and 

 six around the ditrigonal, and the didigonal axes bisect the basal 

 edges between adjacent faces. The solid angles will vary with the 

 value of n, yielding a series of tetrahexahedra, members of which 

 may occur in combination. The form may also be considered as 

 derived from the cube by replacing each face with four triangles. 



