ISO.MKTUIC SVSTI.M 



57 



as produced by the extension of alternate octants of the 



trtr;moii:il t ri>oct:ihedron. There are congruent + and form>. 



IV. Tetragonal tristetrahedron ; 



na : a : a 



K (hhi) K (hhi). 



Let the poles now lie moved on the side of the triangle between 

 the ditrigonal axes, when the tetragonal tristetrahedron bounded 

 l>y 12 tetragonal faces will be pro- 

 duced, Fig. 93. Three faces are grouped 

 around the extremities of the ditrig- 

 onal, four around the didigonal axes. 

 This form may also be derived by ex- 

 tending alternate octants of the trigonal 

 trisoctahedron. 



The four tetrahedral forms thus far 

 considered are variable forms, as their 

 angles will depend upon the value of the 

 intercepts. 



V. If the pole be placed on the didigonal axes, the hexahedron 

 will be reproduced, as in type 32. 



VI. If the pole be placed in the plane of symmetry midway 

 between the ditrigonal axes, the rhombic dodecahedron will be re- 

 produced ; both hexahedra and rhombic dodecahedra may combine 

 with tetrahedral forms. 



VII. Tetrahedron; - ; K (in) c (iii). 



FIG. 93. Tetragonal Tris- 

 tetrahedron, K (221). 



Fiu. 94. Tho Plus Tetrahedron, 



K(lll). 



In.. '.Ma. The Negative Tetra- 

 hedron, ic (111). 



If the poles be placed on the ditrigonal axes, six faces will fall 

 in the same plane, producing a form bounded by four equal equi- 

 lateral triangles, the regular tetrahedron, Fig. 94. It may also be 



