. 147. OF COMBINATIONS. 175 



will require us also to enlarge three alternating faces on the 

 opposite side ; but the enlarged faces may be either those 

 which are parallel to the former, or those which are not 

 parallel to them. 



The first process produces a form exactly similar to a 

 rhombohedron, if considered as a geometrical solid, which 

 nevertheless cannot be considered as a rhombohedron in 

 Crystallography, because in a compound form its faces can 

 never assume the position of the faces of a rhombohedron. 

 A combination in which one or several such forms appear, 

 is more particularly designated by the expression of a hemi- 

 rhombohedral form of parallel faces. In a combination of 

 this kind, particular attention must be given to the situa- 

 tion of the faces, in as much as two such forms similar to 

 a rhombohedron arise from the resolution of a single pyra- 

 mid, whose faces are situated either to the right or to the 

 left of a face of the fundamental form, or of any other 

 complete form contained in the combination. 



The second process yields two forms, contained under 

 irregular trapezoidal faces, which on that account are called 

 three-sided Trapezohedrons. They are equal and similar, but 

 distinguished from each other by the character of being 

 twisted as it were, to the Right or to the Left (. 67. 4.). 

 Fig. 53. represents a Right Trapezohedron, which is pro- 

 duced by the enlargement of the faces, a, a, &c. Fig. 11, while 

 Fig. 54. shews a Left one, which is contained under the 

 faces &, &, &c. of the same pyramid. A combination partly 

 or entirely consisting of such forms, is termed a hemi- 

 rhombohedral one of inclined' faces. The contorted aspect of 

 the trapezohedrons extends likewise to these combinations. 



The same process applied to the isosceles six-sided pyra- 

 mid, gives in the first case, or by means of the enlargement 

 of parallel faces, forms likewise similar to a rhombohedron, 

 which yet, for the reasons mentioned above, cannot be con- 

 sidered as rhombohedrons. If, however, we enlarge those 

 faces, which are not parallel, the result is an isosceles three- 

 sided Pyramid^ Fig. 52. The faces of those rhombohedron- 

 like forms, as well as those of the three-sided pyramids, 



