26 CRYSTALLOGRAPHY. 
and hence it affords an example of hemihedrism—a kind that is 
presented by many crystals of pyrite. Fig. 48 is the hemihe- 

Se 
drval form resulting when these twelve planes 7-2 are extended 
to the obliteration of the cubic faces; and fig. 49 is another, 
made of the other twelve of these planes. Again, 
in fig. 50, a cube is represented having only 
three out of the six planes of fig. 22, and this 
is another example of hemihedrism. These kinds 
differ from the inclined hemihedrons in having 
opposite parallel faces, and hence they are called 
parallel hemthedrons. 

4, Internal Structure of Isometric Crystals, or Cleavage.— 
The crystals of niany isometric minerals have cleavage, or 
a, greater or less capability. of division in directions situated 
symmetrically with reference to the axes. The cleavage direc- 
tions are parallel either to the faces of the cube, the octahe- 
dron, or the dodecahedron, Jn galenite (p. 145) there is easy 
cleavage in three directions parallel te the faces of the cube ; 
in fluorite (p. 208), in four directions parallel to the faces of the 
octahedron ; in sphalerite (p. 154). in.six directions parallel to 
the faces uf the dodecahedron. These cleavages are an impor- 
tant means of distinguishing the species. 
The three cubic cleavages are precisely alike in the ease with 
which cleavage takes place, and in the kinds of surface obtained ; 
and so is it with the four in the octahedral directions, and the six 
in the dodecahedral. Occasionally cleavages of two of these sys- 
tems occur in the same mineral ; that is, for example, parallel to 
both the faces of the cube and the octahedron ; but when so, 
those of one system are much more distinct than those of the 
other, and cleavage surfaces in the two directions are quite un- 
‘like as to smoothness and lustre. 
5. Irregularities of Isometric Crystals,—A cube has its faces 
precisely equal, and so it is with each of the forms represented 
