ITS MODIFICATIONS. 121 



This may be easily conceived, if we recollect that 

 the octahedron itself is a figure resulting from the 

 modification a of the tetrahedron; and that the edges 

 of the modifying plane 0, of the tetrahedron, are not 

 affected by modification e, or f y which replace the 

 primary edges of the tetrahedron ; and that the pri- 

 mary edges of the tetrahedron are not affected by the 

 modifications , and c, which would replace the edges 

 of the modifying plane a. Three classes of modifica- 

 tion must therefore concur upon the tetrahedron, to 

 produce most of the secondary forms of the octa- 

 hedron. 



ITS MODIFICATIONS. 



Primary form. The rhombic dodecahedron. 

 Plane P on P', 90. 

 P on P", 120. 



For the sake of avoiding a frequent repetition of 

 the description of the two kinds of solid angles of this 

 figure, those contained within four acute plane angles 

 will be called the acute solid angles, and those con- 

 tained within three obtuse plane angles, will be called 

 the obtuse solid angles. 



Modifications. 



Class . Acute solid angles replaced by tangent 

 planes. 



The new figure would be the cube. 

 Plane a on P, 135. 



