138 TERMINOLOGY. . 129. 130. 



in the first and second processes ; and then there are no 

 more than three axes of this kind to be found in the solid. 

 In the resolution of halves in fourths, or in the application 

 of two of the methods at once, they disappear entirely. 

 The peculiar character of the halves is, therefore, that they 

 have six axes less ; of the fourths, that they have nine axes 

 less than the original forms. 



The halves arising from the first method of resolution, 

 and the fourths, into the formation of which this method like- 

 wise enters, assume the general aspect of the tetrahedron. 



The crystallographic signs of these forms are obtained 

 by indicating a division by the numbers 2 and 4, the re- 

 ferences as to position by the signs + and , and those to 

 Bight and Left, by the letters r and 1 prefixed to the crys- 

 tallographie sign of the original form. 



. 129. THE TETRAHEDRON. 



The half of the octahedron is the Tetrahedron 

 (. 57.)- 



The octahedron allows of the application of the first pro- 

 cess. The number of faces of its half is four, and these 

 faces are perpendicular to the rhombohedral axes. 



The crystallographic signs of the two tetrahedrons, of 

 which one is in the normal, the other in the inverse posi- 

 tion, Figs. 13. 14., as halves of the octahedron, are - (o) 

 and 5L ((/). 



. 130. THE HEXAHEDRAL PENTAGONAL-DODECA- 

 HEDRON. 



The half of the hexahedral trigonal-icositetrahe- 

 dron is the hexahedral Pentagonal-dodecahedron 

 (. 66.). 



Here the second process must be applied. If the al- 



