66 CLEAVAGK. 



tetrahedron containing this minute octahedron. The 

 tetrahedron would obviously be reducible to the oc- 

 tahedron, as other tetrahedrons are, by the removal 

 of all its solid angles. 



But it is apparent that the solid angles to be re- 

 moved in this instance, are the small cubes a e g t, 

 and by their removal the octahedral solid shewn in 

 fig. 96 will remain. 



This octahedron is supposed to rest on one of its 

 planes, and the molecules b c, c h, /c, c d, may be 

 conceived to constitute four of its edges. 



Thus the necessity of adopting the tetrahedron as 

 the molecule of the octahedron is removed, and in 

 consequence a more simple theory of the structure 

 of the octahedron, may be substituted for that which 

 has been established upon the adoption of tetrahedral 

 molecules. 



By a similar mode of reasoning, the compatibility 

 of the cubic molecule with the solids obtained by 

 cleavage from the rhombic dodecahedron, might be 

 shewn; and by adopting the cubic molecule, a more 

 simple theory of decrement, in relation to the rhom- 

 bic dodecahedron, may be substituted for that which 

 has been established upon the assumption of the 

 irregular tetrahedron as the integrant molecule, and 

 the obtuse rhomboid as the subtractive molecule. 



