. 115. OF THE CONNEXION OF FORMS. 119 



the pyramids, so that only the central part analogous to 

 that in . 111. remains, to which the lateral edges are ad- 

 jacent. 



This part contains one-third of the axis of the rhom- 

 bohedron, from which the pyramid is derived. It is limit- 

 ed perpendicularly to the axis by equilateral hexagons, 

 whose alternating angles are equal (. 1 13.), and from the 

 sides by twelve scalene triangles, whose bases are the sides 

 of those hexagons, the longer sides being the entire lateral 

 edges, and the shorter sides parts of the obtuse terminal 

 edges of the scalene six-sided pyramid. 



The central part of a pyramid derived according to the 

 same m from a more acute rhombohedron, although con- 

 tained under faces of the same kind, will yet differ from 

 the preceding by the sum of the angles at the base of the 

 triangles being greater, the angle at the vertex smaller, 

 and the sides approaching nearer to parallelism and equa- 

 lity with each other, and to one-third of the axis of the 

 rhombohedron. 



The limits to which the pyramids approach, when thus 

 derived according to the same m, from more and more acute 

 rhombohedrons, are : the sum of the angles at the base of 

 the triangles must be = 180, the angle at the vertex = ; 

 and the sides equal and parallel among themselves, and 

 to one-third of the axis of the rhombohedron. These li- 

 mits are obtained when the central part of the pyramid, 

 containing one-third of the axis of the rhombohedron, 

 from which the pyramid is derived, and therefore the axis 

 of the rhombohedron itself becomes infinite, or when the 

 rhombohedron is changed into the regular six-sided prism. 

 If therefore (P 4- n) m is changed into a prism, the expres. 

 sion of its axis 2 n . m. a, will be changed into 2* . m. a, because 

 n and not m is = oo> 



While the scalene triangles, the lateral faces of the cen- 

 tral part, by the continual increase of the axis, are chang- 

 ed into unlimited parallelograms, the central part itself 

 is changed into a twelve-sided prism, unlimited in the direo 

 tion of the axis. Through all these changes, however, m 



