30 



STRUCTURE OF MINERALS. 



rived from one another. Figure 22 represents an octahedron 



with the edges truncated. On 

 continuing this truncation, the 

 planes A are reduced in size, 

 and the form in figure 22a is 

 obtained; and another step be- 

 yond, we have the dodecahedron, 

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

 sents a dodecahedron with 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 the angles 

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

 diagonal of the prism ; the form in 

 figure 23 is first obtained, and final- 

 ly a square octahedron, figure 23a. 

 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 

 24 24a 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 pi ism, 

 (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. 25a) ; and conversely cut off the lateral edges 



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

 rhombic octahedron from a rhombic prism ? How a rectangular prism 

 from a rhombic 1 



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