PASSAGE OF ONE FORM INTO ANOTHER. 



51 



The Tetrahedron may be derived from the Cube and from the 

 rhombic Dodecahedron, by means of the tangent replacement of 

 half of the similar parts of these solids which exist to the number 

 of eight. 



Many species of minerals present crystals which exemplify this 

 passage of one form into another, according to the symmetrical 

 modification^ just noticed. Thus, Fluor and Sulphuret of Silver 

 are crystallized under the different forms of the Cube, the regular 

 Octahedron and the rhombic Dodecahedron; the Diamond and Red 

 Oxide of Copper under the same; and Blende under the Octahedron, 

 the Dodecahedron and the Tetrahedron. 



In the transitions into each other of the solids just enumerated, in 

 consequence of the symmetrical modifications they undergo, we 

 have seen that they were the result of tangent replacements. We 

 will now notice some of the new forms produced upon these forms 

 by the operation of other modifications. 



It has been seen that the truncation of all the edges of the Cube 

 by tangent planes would result in the rhombic Dodecahedron. If, 

 however, the edges be replaced by single planes, inclining at une- 

 qual angles on the adjacent primary planes, 

 a series of Dodecahedrons with pentagonal 

 faces would be the result.* Fig. 121 illus*- 

 trates this transition of the Cube into the 

 Dodecahedron with pentagonal faces : the 

 new planes k, are not produced so as com- 

 pletely to obliterate the faces P of the ori- 

 ginal Cube. 



The replacement of the edges of the Cube by two planes produ- 

 ces a series of four sided pyramids on the planes of the Cube. Fig. 

 123 shows this passage of the Cube into a form contained under 

 twenty four planes. The primary faces are represented, in the fig- 

 ure, as nearly extinguished. The new form produced in this way, 



Fig. 122. 



There is only one of the series, Fig. J.22, 

 to exist among crystals. 



