. 117. OF COMBINATIONS. 177 



nations of inclined faces is a six-sided Trapezohedron^ a solid 

 contained under twelve equal and similar trapezoidal 

 faces. Pairs of them are obtained by enlarging the alter- 

 nating faces contiguous to one of the apices, and those of 

 the other which are not parallel to them ; they shew, like 

 some of the forms considered above, the differences of 

 Right and Left. A Right Trapezohedron of this kind is 

 represented in Fig.SJ., a Left one in Fig. 58. The first is 

 obtained by enlarging the faces, a, a ; and a', a', &c. ; the 

 second, by enlarging the faces marked &, b ; and &', &', &c. 



The three-sided trapezohedrons, Figs. 53. and 54., are 

 obtained by enlarging all those faces of the six-sided ones 

 which are marked a, a, &c. or &, J, &c. in Fig. 51. ; but if 

 we enlarge the faces , , &c. or b 7 &, &c. contiguous to the 

 upper apex, and the faces a', a', &c* or V, &', &c. conti- 

 guous to the lower apex, forms will result, like Fig. 55. 

 and Fig. 5C., and which are right and left trapezohedrons 

 like the former, but which contain faces of the scalene 

 six-sided pyramids in both positions. The situation of 

 these faces determines their existence in the combinations. 



In order to re-obtain the simple forms from a di-pyramid, 

 it is necessary to enlarge the alternating pairs of faces, 

 a and 6, or those which meet in the obtuse terminal edges 

 of the six-sided pyramid from the upper apex, and the al- 

 ternating ones, a and 6 from the lower apex. If, on the 

 contrary, we enlarge those on the lower apex which pro- 

 duce with the former horizontal edges of combination 

 like a' and &', the result will be scalene six-sided py- 

 ramids, whose bases are hexagons of alternately equal 

 angles, similar to the figure produced by a section perpen- 

 dicular to the axis which does not intersect the lateral edges. 

 Simple minerals may assume this form, although they have 

 as yet not been found in nature ; but they are very com- 

 mon in compound minerals, and as such they will be the 

 subject of farther investigations. 



Hemi-rhombohedral and hemi-di-rhombohedral combina- 

 tions occur in rhombohedral Fluor-haloide, and in rhombo- 

 hedral Quartz. 



VOL. I. M 



