Theory of CryflaUlzatwn. 4* 



J£P [fig. 5) to reprefctit a dodecaedron, whofe faces are 

 equal and fimilar rhombufes; and that this dodecaedron is a. 

 Secondary form, which has a cube for its nucleus or primitive 

 form. The pofition of this cuoe may be eafily conceived 

 by infpecling fig. 6, where.it is feen that the fmall diagonals 

 DC, CG, GF, FD, of the four faces of the dodecaedron, 

 united around the fame folid angle L, form a fquare, CDFG. 

 But there are fix folid angles compofed of the four planes, 

 viz. the angles L, O, £, N, R, P, (fig. 5) ; and, confe- 

 quently, if feetions are made to pafs through the fmall diago- 

 nals of the faces which concur to the formation of thefe 

 folid angles, we fhall fuccelfively uncover fix fquares, which 

 ■will be the faces of the primitive cube, and three of which 

 are reprefented (Jig. 6), viz. CDFG, ABCD, BCGH. 



This cube would evidently be an affemblage of integral 

 cubic moleculae, and it would be neceffary that each of the 

 pyramids, fuch as LDCGF (fg. 6), which reft on the faces, 

 fhould itfelf be compofed of cubes equal to each other, and 

 to thofe forming the nucleus. 



To make it more apparent how this might take place, I 

 fhall point out the means of making an artificial dodecaedron, 

 by employing a certain number of fmall cubes, the aflbrtment 

 of which will be an imitation of that of the moleculae em- 

 ployed by nature in the formation of the dodecaedron we 

 are here confidering- 



Let ABGF (Jig. 7) be a cube compofed of 729 fmall 

 cubes equal to one another, in which cafe each face of the 

 whole cube will contain 8 1 fquares, nine on each fide, which 

 will be the external faces of as many partial cubes, reprefenta- 

 tives of moleculae. The cube in queftion will be the nucleus 

 of the dodecaedron which we propofe to conftrucl:. 



On one of the faces, fuch as ABCD of this cube, let us 

 apply a fquare lamina compofed of cubes equal to thofe 

 which form the nucleus, but which towards each edge has a 

 jangeof cubes lefs than if it had been on a level with the 

 adjacent faces BCGH, DCGF, &c. That is to fay, let this 



lamina 



