Theory of Cryfial.'ifatwt:. 299 



triangles, fituated, two and two, above the fix faces of the 

 fame nucleus. If we had a dodecaedron fimilar to that of 

 fig. 20, and wifhed to convert it geometrically into an ico- 

 faedron, fuch as that in queflion, it would be fufficient to 

 make the planes of eight feclions pafs through it in the fol- 

 lowing manner, viz. one through the three angles P, N, L, 

 (fig. 19.), another through the angles P, M, S, a third 

 through the angles L,R,U, &c. A comparifon of the figures 

 19 and 55 will fhew, by the correfpondence of the letters, 

 the relation between the two polyedra ; but this is an ope- 

 ration merely technical, to which nature could not defcend. 

 I (hall obferve, befides, that the nucleus of the icofaedron, 

 to which we fiiould arrive, would be much fnialler than that 

 of the dodecaedron, fince the folid angles of the latter nu- 

 cleus would be confounded with the angles D, C, G, &c. 

 (fig. 20.) of the dodecaedron; whereas the other nucleus 

 would have its folid angles fituated in the middle of the 

 equilateral triangles MPS, NPL, URL, Sec. (fig. 55.). 



The icofaedron of the fulphure of iron has been con- 

 founded with the regular icofaedron of geometry, which 

 differs from it very fenfibly, fince all its triangles are equi- 

 lateral. It is demonftrated by theory, that the exiftence of 

 the latter icofaedron is as impcfhble in mineralogy as that of 

 the dodecaedron ; fo that among the five regular polyedra of 

 geometry, viz. the cube, the tetraedron, the oftaedron, the 

 dodecaedron, and the icofaedron, the three former only cart 

 exifl there, in confequence of the laws of cryftallifation. It 

 is not uncommon therefore to find them among cryftals of 

 various kinds of minerals. 



The icofaedron of the fulphure of iron is much lefs com- 

 mon than the dodecaedron. It is found in folitary cryftals. 

 I have one which is complete, and about half an inch in 

 thicknefs. 



Polytu 



