TERMINOLOGY. . 156. 



head. Every thing necessary to know of them follows im- 

 mediately from their derivation from the hexahedron, if 

 \ve only attend to the different positions, which the faces 

 of the forms combined assume in respect to the different 

 axes. Hence even the angles of incidence at the edges of 

 combination may immediately be deduced for those forms 

 whose dimensions are invariable, their faces being perpen- 

 dicular to one of the three kinds of axes (. 40.). For 

 these angles of intersection between the faces of such 

 forms, and the angles at the centre produced by those 

 axes, which are perpendicular to these faces, must be sup- 

 plemental to each other. The algebraic formulae given for 

 the different systems of variable dimensions, may also be 

 employed for obtaining the angles both of simple forms 

 and of combinations of the tessular system. For this pur- 

 pose, the simple forms peculiar to the tessular system, or 

 rather parts of them contained under faces similarly situ- 

 ated in respect to a single axis considered as the principal 

 one, may be considered as forms belonging to one of the 

 preceding systems. In this case every thing applies to 

 them, that has been above stated in respect to binary com- 

 binations. If, for instance, the hexahedron be considered 

 as a rhombohedron = It ; the horizontal faces of the octa- 

 hedron will represent R co, the inclined ones R + 1 ; 

 and the combination of the hexahedron and the octahedron 

 supposed to be a rhombohedral combination, will be ex- 

 pressed by II co. R. R + 1. As a tessular combina- 

 tion, its crystallographic sign is H.O (. 121. 124.). If we 

 consider the octahedron as an isosceles four-sided pyramid 

 of the pyramidal system, and designate it accordingly by 

 P, the horizontal faces of the hexahedron will assume the 

 situation of P co, while the vertical ones assume that of 

 [P + co] ; thus, for the sake of applying the calculations, 

 P eo. P. [P 4- co] will express the same combination 

 of the hexahedron and the octahedron. 



This process also extends to combinations produced by 

 more than two simple forms. Suppose, for instance, a com- 

 bination of the hexahedron, the octahedron, the dodecahe- 



