ITS MODIFICATIONS. 113 



t 



there is only one of the series known to exist among 

 crystals. 



It appears that in all these irregular modifications, 

 only one half the number of modifying planes is pro- 

 duced, which would be required by the law of sym- 

 metry. 



ITS MODIFICATIONS. 



Primary form. The regular tetrahedron 

 Plane P on P', 70 31' 43". 



Modifications. 



Class . Solid angles replaced by tangent planes. 



When the modifying planes first touch each other on 

 the edges of the tetrahedron, a regular octahedron is 

 produced. 



When the primary planes are entirely effaced, the 

 new figure is a tetrahedron similar to the primary. 



Plane a on P or P', 109 28' 16". 



Class b. Solid angles replaced by three planes 

 resting on the primary planes. 



The new figures would be dodecahedrons, gene- 

 rally with trapezoidal planes ; but one individual 

 modification belonging to this class produces the 

 rhombic dodecahedron. 



