30 



STRUCTURE OF MINERALS. 



rived from one another. Figure 22 represents an octahedron 



22 22a with the Vfges truncated. On 

 /\\ continuing this truncation, the 



plants A are reduced in size, 

 ana the form in figure 22a ig 

 btained; and another step be- 

 yond, we have the dodecahedron, 

 (fig. 21 b.) Figure 22a repre- 

 sents a dodeca' edron/Vvith the obtuse solid angles replaced ; 

 and this replacement continued, produces finally an octahe- 

 dron, the reverse of the preceding. 



These solids are, then, so related that they are all deriva- 

 ble from one another ; and the three actually are often pre- 

 sented by the same mineral. All the figures above referred 

 to, occur as forms of galena, fluor-spar, and several other 

 species. Instead, therefore, of considering the three solids, 

 the cube, regular octahedron, and dodecahedron, as indepen- 

 dent forms, we properly speak of them as constituting to- 

 gether one system, or as belonging to the same series of 

 forms. 



Again : pursue the same mode of dissection on tjrle angles 

 of a square prism, taking care to move the knife rafrallel to a 



23 23a diagonal of the prism ;/the form in. 

 f s p ~"Z >\ /k\ figure 23 is first obtained, and final- 



( Y /a/J\a\ ly a square octahedron, figure 23a. 



L.U4fe==c22^:-A7 The square prism and square octa- 

 hedron (like the cube and regular 

 octahedron) belong to one and the 

 same system. The two often oc- 

 cur in the same mineral. 



Again : remove with a knife the basal edges of a rhombic 

 prism, moving the knife parallel to a 

 diagonal plane of the pi ism, figure 24 

 is at first obtained, and then a rhombic 

 octahedron, (fig. 24a.) Remove the 

 four lateral edges of a rhombic prism, 

 (see fig. 26a,) keeping the knife paral- 

 lel to a vertical diagonal plane : the 

 form in figure 25 will first be obtained, and then a right rectan- 



gular prism, (fig. 2 



iq) : and conversely cut off the lateral edges 



How can you make a square octahedron from a square prism 1 How 

 rhombic octahedron from a rhombic prism ? How a rectangular prism 

 troin a rhombic I 



