192 [June 19, 



three-faced octahedron, the one group being derived from the faces 



kkh, Ikh, Ikh, k~kh 



kkJi, kkh, kkh t kkh, 

 the other from 



hhk, Ihk, hhk, hh_k_ 



hhk, hhk, hhk, hhk. 



The tritohedral development of the form h k I gives the ditetragonal 

 pyramid ; of these there are three groups. 



1st. klh, Ikh, Ikh, klh, klh, ilk, Ikh, klh 

 klh, Ikh, Ikh, 111, klh, Tkli, Ikh, klh. 



2nd. hlk, Ihk, Ihk, hlk, ~hlk, Ihk, Ihk, hlk 

 hllc, Ihk, ~lhk, lilt, hlk, Ihk, Ihk, hlk. 



3rd. hkl, khl, khl, hkl, hkl, III, kll, hkl 

 hk~l, khl, ~khl, hkl, hkl, khT, khl, hkl. 



Ditetragonal pyramids may also be developed from the faces of 

 the forms hhk and k k h, whose poles lie in the zones 01 1, 100, 

 and 1 1, 1 0. 



The forms of the hexagonal system are regarded as tetartohedral 

 developments of the cubical system, the groups of faces being always 

 taken symmetrically with respect to the diagonal of the cube or one 

 of the octahedral axes. 



The two faces of the octahedron 111 and TIT thus form the 

 basal pinacoids. 



The six faces of the rhombic dodecahedron 



101, Oil, 110, 1 01, Oil, and 110 



give one hexagonal prism, while the other is derived from six faces 

 of the twenty-four-faced trapezohedron, whose symbols are 



2lT, 112, 1 21", 211, Tl2, 121. 



The dihexagonal prisms are derived from those faces of the form 

 hkl which lie in the zone 1 1, 2 1 1 . 



There are three groups of positive rhomboids, two derived from 

 the three-faced octahedron, and one from the twenty-four-faced 

 trapezohedron. 



