87 



limiting faces, and are usually called: tetrahedral-pentagonal-dode- 

 cahedron, pentagonal-icositetmhedron (gyroid), dyads-dodecahedron 

 (didodecahedron\ diploid), hextetrahedron, and hexoctahedron respec- 

 tively, and their general Millerian symbol is {hkl}. 



In the cubic system the three planes passing through every 

 pair of the perpendicular binary or quaternary axes, parallel to the 

 edges of a cube, are always taken as coordinate-planes. If now the 

 stereographical projection of a limiting face of the form considered, 

 should happen to coincide with the point of intersection of the sphere 

 with one of the coordinate-axes, or if it be situated in one of 

 the coordinate-planes, etc., or if that face be parallel to a coordinate- 

 axis or to a coordinate-plane, then the symmetrical repetition of 

 that face will determine a simple form of each crystal-class, which 

 does no longer agree with the most unrestricted, general form of 

 that class. These new simple forms, on the contrary, will possess less 

 limiting faces than the most unrestricted one, and therefore will 

 have a simpler shape and a simpler Millerian symbol. In the next 

 table a review is given of the special cases mentioned for every class 

 of the regular system, and the corresponding Millerian indices for 

 every form are there indicated also. 



The constant forms, occurring in all classes of the system, are: 

 the cube {100} , and the rhombicdodecahedron {no} , while the octa- 



