176 TERMINOLOGY. . 147. 



keep the situation of those of the isosceles six-sided pyra- 

 mid, from which they are derived, and appear as such in 

 the combinations ; and this is the character by which they 

 may be recognised. The combinations themselves receive 

 the same denominations as above. 



The regular six-sided prism P + co may assume a hemi- 

 rhombohedral aspect, like a finite isosceles six- sided pyra- 

 mid. In this case its faces must be symmetrically distri- 

 buted in the combination, like those of an equilateral three- 

 sided prism in a position which is characteristic and pecu- 

 liar to it. 



If the unequiangular twelve-sided prism enters a hemi- 

 rhombohedral combination, its faces likewise must be sym- 

 metrically distributed, which comprises two cases. By en- 

 larging the alternating faces, it will appear either as a regular 

 six-sided prism, different from R + co and P + co by its 

 position ; or by enlarging the alternating pairs of faces, it as- 

 sumes the aspect of a six-sided prism, whose alternating 

 angles only are equal. 



The rhombohedron itself may produce a hemi-di-rhombo- 

 hedral combination, but only one of inclined faces, because 

 if the parallel faces of the di-rhombohedron are enlarged, 

 the rhombohedron will be reproduced, and the combina- 

 tion itself will be simply rhombohedral (. 145.). The re- 

 suit is an isosceles three-sided pyramid, differing both in 

 position and dimensions, from that which may be obtained 

 from the isosceles six-sided pyramid. In the same way 

 the di-pyramid (. 146.) also enters into a hemi-di-rhom- 

 bohedral combination, although its halves and fourths may 

 appear both as forms of inclined faces, and as forms of pa- 

 rallel faces. For if we enlarge the alternate faces conti- 

 guous to the upper apex of the di-pyramid, and those con- 

 tiguous to the lower apex, which are parallel to the former, 

 two forms will arise, which, though exactly similar to iso- 

 sceles six-sided pyramids, are yet different from these forms 

 in respect to the situation of their faces. Combinations of 

 this kind are said to be hemi-di-rhombohedral of parallel faces. 

 The characteristic form of the hemi-di-rhombohedral combi- 



