CRYSTALLIZATION. 93 



453. The simplest angular body must be circum- 

 scribed by at least four surfaces, and thus be a tetra- 

 hedron. 



454. The fundamental nucleus of crystals is, however, 

 the double tetrahedron or the hexahedron, namely the 

 trilateral double- pyramid ; for radii do not proceed simply 

 from the point of commencement, but also from the ex- 

 tremities of the axis. When the superior and inferior 

 radii meet, they must form a double-tetrahedron. The 

 disposition to this form has been implanted in all crystals. 

 If the nucleus becomes no such hexahedron, the aber- 

 ration from, still admits of being referred to, the hexa- 

 hedron, i 



455. There is no prismatic nucleus. The columns 

 and parallelepiped nuclei are only mutilations. 



456. The tetrahedron is also only a mutilated nucleus. 

 To the essence of a nucleus belong two tetrahedra, with 

 their bases joined to each other. 



457. The six-sided double-pyramid is a duplication of 

 the hexahedron. The octahedric nuclei, are things inter- 

 mediate between the three- and six-sided interruptions of 

 the natural type, like quadrinumeral or tetrapetalous co- 

 rolla? in flowers. 



458. Columns originate only between the two tetra- 

 hedra, without doubt owing to deficiency in bulk. 



459. If the three-sided double-pyramid be the pri- 

 mary form of crystals, so must the six-sided column with 

 trilateral terminal pyramids be the ultimate form. The 

 rhomboidal-dodecahedron is therefore the most perfect 

 crystal. It is the most perfect representation of the 

 globe in the angular form. 



460. The crystal can not commence with the nucleus 

 and then for the first time continue to grow or even 

 change into the perfected crystal, because it becomes only 

 crystal in the conflict of the linear and spherical action. 

 As little as the sun can be produced without the planet, or 

 vice versa, so little can a nucleus subsist without what is 

 called the external shell or crust. The nucleus is in fact 

 determined by the shell of the crystal, namely by the 



