CRYSTALLOGRAPHY 



25 



form. The set of parameters a:a:3a represents three faces in 

 each octant , a> In-re the axes are interchangeable and when one axis 

 i- cut all mu-t \H> cut by a plane 

 at : : ; 1 1 lese 1 1 iree planes are rep- 

 re-euted 1 >y (a. : a \ 3 a), (a : 3 a : a), 

 (3a:a:a), or 24 faces in the 

 eight octants; Fig. 33 repre- 

 sents this form. 



Hemihedral form is the term 

 used to denote those types in 

 which the symmetry requires 

 only one half of the faces pos- 

 sible to be represented by one 

 set of parameters, to be present 

 to complete the form. There 

 are several classes of hemihe- 

 drons, according to their symmetry. If the most general form of 

 a system as (a : 2 a : 3 a), represented by Fig. 34, with 48 faces, is 

 taken, there may be numerous ways of selecting one half of these 

 48 faces; the symmetry of the types allows but three to form 

 hemihedrons. 



I. By taking all the faces in alternate octants and extending them 

 until they inclose space, as the shaded faces of Fig. 35, which when 



Fro. 34. The Hexoctahedron, 

 a : 2 a : 2 a. 



Fiu. 35. 



FIG. 36. 



extended will produce the form represented in Fig. 36. Since some 

 holohedrons have a center of symmetry and are formed of pairs of 

 parallel faces; this class of hemihedrons in which one face of each 

 pair of faces of the holohedron is extended, will not be formed of 



