44 TIUIMINOLOGY. . 52. 



7- The term Pyramid has not exactly the same signifi- 

 cation in Crystallography, as in Geometry. In Geometry, 

 it means a solid, bounded by any number of triangular 

 planes meeting in one point, and terminating at one poly- 

 gonal plane, as its base. In Crystallography, it must be 

 restricted to simple forms ; and, therefore, cannot be ap- 

 plied to any other but those, which have hitherto been call- 

 ed double pyramids. There are no simple pyramids, as 

 simple forms, to be considered in Crystallography. The te- 

 trahedron, which has been called a simple three-sided pyra- 

 mid, is no pyramid at all, but is a form of several axes, and 

 in the closest connexion with other forms of that kind, 

 particularly with the octahedron. The epithet double, there- 

 fore, is superfluous, since the crystallographer has on no oc- 

 casion to distinguish between simple and double pyramids, 

 as two different classes of simple forms. 



. 52. ISOSCELES FOUR-SIDED PYRAMIDS. 



The isosceles four-sided pyramids, Fig. 8., are 

 contained under eight isosceles triangles. 



1. The isosceles four-sided pyramids, have two principal 

 flections, one of which, BCB'C', is a square, the other, 

 ACXC, or AB'XB, a rhomb. 



2. The remaining sections, belonging to the principal 

 axis, are also squares ; and the axis is therefore of the se- 

 cond kind (. 40.). This axis itself, the solid angles through 

 which it passes, and the sections belonging to it, are term- 

 ed Pyramidal^ because all forms in connexion with the isos- 

 celes four-sided pyramid, contain axes, solid angles, and sec- 

 tions of the same kind. The same denomination applies to 

 every form possessing similar axes, solid angles, and sec- 

 tions, although this form be not an isosceles four-sided py- 

 ramid. 



3. Besides these, the isosceles four-sided pyramids con- 

 tain four axes of the third kind, two of which, BB' and 

 CC', are the diagonals, the two others HH'" and H'H" 



