56 



MINERALOGY 



rahedron correspond to one half the poles of hexoctahedron. It is 

 as if all the faces in alternate octants above and below were extended 

 (Fig. 35, the shaded octants) until they inclosed space ; the form 

 produced would be the + hextetrahedron. When the unshaded 

 faces are extended the hextetrahedron is produced, congruent 

 with the former by a revolution of 90. In all hemihedrons there 

 are + and , or right and left forms, which may occur on crystals 

 in combination, or independently. forms are always congruent 

 by a revolution. 



Other forms of this type may be produced, as in the holohedral 

 class, by moving the pole of the most general form to the sides and 

 angles of the triangle in which it lies, yielding in all seven possible 

 forms, some of which will be new forms ; others will be of the same 

 shape as the holohedral forms. 



II. In Fig. 91, if all the poles be moved till they lie on the side of 

 the triangles between the two didigonal axes, they will occupy the 

 same position as, Fig. 75, the poles of the tetrahexahedron. The 

 holohedral and hemihedral forms are of the same shape, but the 

 symmetry of the two, caused by the character or arrangement of 

 the molecules, will differ. Where an apparent holohedral form is 

 found in combination with hemihedral forms, it must be considered 

 as a hemihedron and will possess the lower type of symmetry. 



The tetrahexahedron is reproduced by extending the faces which 

 exist in alternate octants, as each face of the holohedral form 

 extends in two octants, half in each ; the half lying in the octants 

 extended will reproduce the half in the adjacent octants. There 

 are no + or forms in those cases where the hemihedron assumes 

 the holohedral shape. 



T13. * fl * Tlfl. 



III. Trigonal tristetrahedron ; - - ; K (hhl) K hhl). 



If the poles be placed on the side 

 of the triangle between the ditrigonal 

 and didigonal axes, two will coincide, 

 yielding a new form, the trigonal 

 tristetrahedron, bounded by 12 simi- 

 lar isosceles triangles, Fig. 92. Three 

 faces are grouped around one ex- 

 tremity of the ditrigonal axis and 

 6 around the other. The didigonal 

 axes bisect the base of the triangu- 



FIG. 92. The Plus Trigonal Tris- 

 tetrahedron. lar faces. This form may also be 



