PASSAGE OF ONE FORM INTO ANOTHER. 



53 



Fig. 127. 



It flows also from the regular Octahedron, through the replace- 

 ment ofits solid angles by four planes resting on the primary planes, 

 and from the rhombic Dodecahedron through the tangent replace- 

 ment of its edges. (Fig. 65.)* 



If the Cube have its solid angles 

 replaced by six planes, (Fig. 60,) 

 the new figure will be contained 

 under forty eight triangular planes. 

 Fig. 127. 



The replacement of the solid an- 

 gles of the regular Octahedron by 

 eight planes, leads to the same re- 

 sult; as likewise the replacement of 

 the edges of the rhombic Dodecahe- 

 dron by two planes. (Fig. 66.) 



The foregoing derivations are abundantly exemplified among the 

 crystals of minerals. The passage of the Cube into the pentagonal 

 Dodecahedron occurs in Iron Pyrites and Grey Cobalt; the deriva- 

 tion of the twenty four sided isosceles triangular form, is seen in the 

 crystals of the Diamond and Sulphuret of Iron; the Trapezohedron 

 flows from the Dodecahedron in Garnet and from the Cube in Anal- 

 cime ; and the last mentioned solid under forty eight triangular 

 planes, occurs among the crystals of Fluor. 



The Octahedron with a square base passes into another Octahedron 

 with a square base, by the replacement of the edges of the pyramids 

 by tangent planes, (Fig. 69); the new octahedron is more obtuse 

 than the primary. This modification occurs in Sphene. The tan- 

 gent replacement of the edges, or of the angles of the base, (Figs. 

 70, 71,) give rise to the right square Prism; a result of frequent 

 occurrence in Zircon crystals. 



The Octahedron with a rectangular base is capable of giving rise 

 to an Octahedron with a rhombic base, by the replacement of the 

 edges of the pyramids by single planes. (Fig. 73.) 



The Octahedron with a rhombic base passes into the rhombic prism, 

 by the replacement of the edges of the base by tangent planes, (Fig. 

 74.) We have this modification in Sulphur. 



The right square Prism, according to the symmetry of its modifi- 

 cations, produces, either another similar right square Prism by the 



* This, though an instance of tangent modification, was deferred to be 

 mentioned here. 



5* 



