Gn Crystallography . 297 



five regular solids, namely, the cube, the octahedron, the 

 tetrahedron, the dodecahedron, and the icosahedron. Na- 

 ture only produces the three t'oinier, and is not susceptible 

 of producing any thing else : among an infinity of diflVrent 

 approximations, which she might present on the subject 

 of the two otht-rs, she stops at that which depends on the 

 simplest laws of decrements, in such a manner that her dode- 

 cahedron and icosahedron are reallv the most perfect and 

 most regular of all the principles of geometrv. 



VVe shall cite a new example drawn from the regular 

 be.xahedral prism of carbonated lime. From what we have 

 said (page JOi) on the method of mechanically dividino- 

 this polyhedron, it is easy to conceive that its rhoniboidal 

 nucleus A A' (fig. H) has its solid lateral angles E, O, I, 

 Kj G, H, situated in the middle of the panes of the prism 

 m d, m' d' ; from which it follows that these angles are the 

 points of departure of the decrements which have produced 

 ihe same panes. 



These decrements act at once on the three plane ar.gles 

 EOT, EOA', 10 A', which concur in the formation of 

 one and the same solid angle ; biu in applying here 

 the observation made with respect to the dodecahedron 

 v/ilh pentagonal faces (page 213), and more particularU' 

 with respect to the regular octahedron (page 223), we can 

 confine ourselves to the consideration of the decrement re- 

 lative to one only of the three ancles in question, by sup- 

 posing that the face which results from it is prolonged on 

 the two rhombs adjacent to that to which this angle be- 

 longs. 



This being granted, let us refer the whole to the six 

 angles E Q I, E H G, I KG, H G K,, OIK, HtO, the 

 first three of which look towards the summit A, and the 

 three others towards the summit A'. If we sup]>osc a de- 

 crement by two ranges of rhomboidal molecules on these 

 difTeicnt angles, it will give rise to six faces which will be 

 parallel to the axis, as we have already shown. 



The lamina; of superposition, at the same time that thev 

 will decrease towards their inferior an<rlc's, will be extended 

 on the contrary by their upper parts, so as to remain al- 

 ways contiguous to the axis, the kiigih of which will of 

 itself go on increasing. Besides, the hiGcts prt)duced by the 

 decrement will grtuliially increase ; and at the tern) where 

 they meet, we shall have the solid A A' (fig. 4), where 

 each of these facets, sucha;;oOy, is design.-Wed by the 

 game [titer as the angle O (fig. b), to which it is referred, 



since 



