55. OF SIMPLE FORMS IN PARTICULAR. 47 



2. The remaining sections are rhombohedral (. 50.) ami 

 prismatic (. 53.), as also the axes. Of the prismatic axes, 

 three HZ, ON and RT pass through the lateral solid angles, 

 and three IS, KU and LV through the centres of the la- 

 teral edges. 



3. The horizontal projection is equal and similar to the 

 base, or to the rhombohedral principal section. 



4. The side of the horizontal projection being = 1 

 (. 50. 12.), let the axis be = m.a (the axis of a rhombo- 

 hedron being designated by a, and a certain constant co- 

 efficient by m) ; the terminal edge = x ; the lateral edge 

 =2 z : we have 



t 2 + 6 

 i 2 + 6 



m 2 . a 2 3 



cos. z 



(m 2 . a 2 3 \ 

 l 

 m 2 . a 2 + 3 / 



. 55. SCALENE SIX-SIDED PYRAMIDS. 



The scalene six-sided pyramids, Fig. 11., are 

 contained under twelve scalene triangles. 



1. The principal section A'BX'C, &c. is a rhomboid. 



2. The remaining sections are rhombohedral; those 

 which pass only through terminal edges are equilateral 

 hexagons of alternately equal angles ; that through the 

 centre, or the transverse section, is an equilateral dodeca- 

 gon, likewise of alternately equal angles. 



3. The lateral edges of this form are disposed like the 

 lateral edges of a rhombohedron. 



4. The horizontal projection is a regular hexagon. 



5. The side of the horizontal projection being = 1 ; let 

 the axis A'X' be = m.a (where a signifies the axis AX of 

 a rhombohedron, whose lateral edges coincide with the la- 

 teral edges CB, BC, &c. of the pyramid, and m a variable 

 co-efficient) : the obtuse terminal edge = y ; the acute ter- 

 minal edge = x ; the lateral edge = z : the following for- 

 mulae will be derived. 



