384 Theory of CryJlallifatiom 



the fmall diagonals of the rhombufes of the dodecaectron, 

 viz. thofe which would be drawn from C to G, from A to 

 J, from C to B, &c. and others would correfpond with the 

 different ridges EC, GP, P L, EA, See. 



1. The planes then of the feftions pafling through the 

 fides and through the fmall diagonals of the twelve rhom- 

 bufes will fubdivide the whole furface into 24 ifofceles tri- 

 angles, which will be the halves of thefe rhombufes. 2. Sinc£ 

 the planes of the fefitions pafs alfo through the centre of the 

 cryftal, they will detach 24 pyramids with three face??, the 

 bafes of which, if we choofe, will be the external triangles 

 that make a part of the furface of the dodecaedron, and of 

 which the fummits will be united in the centre. 



Moreover, if we take, for example, the fix tetraedra which 

 have for external faces the halves of the three rhombufes 

 C E D L, CLGH, CEBH, thefe fix tetraedra will form 

 a rhomboid reprefented hy Jig. 69, and in which the three 

 inferior rhombufes DLGS, GHBS, DEBS, refult 

 from three divifions which pafs, one through the hexagon 

 DLGOBA {Jig. 68.); the fecond through the hexagon: 

 GPIBANF, and the third through the hexagon BEDFPO. 

 Fig. 69 reprefents alio the two tetraedra, the bafes of which 

 make part of the rhombus CLGH. One of thefe is marked 

 by the letters L, C, G, S, and the other by the letters H, C, 

 G, S. By applying what has been faid to the other nine 

 rhombufes, which are united three and three around the 

 points F, A, PI (Jig. 69.), we fhall have three new rhom- 

 boids ; from which it follows, that the 24 tetraedra, con- 

 fidered fix and fix, form four rhomboids ; fo that the dode- 

 caedron may be conceived as being itfelf immediately com- 

 pofed of thefe four rhomboids, and in the laft analylis of 24 

 tetraedra. 



I {hall here obferve, that the dodecaedron haying eight folid 

 angles, each formed by three planes, we might have confi- 

 dered them as being the aflemblage of the four rhomboids, 

 which would have for exterior fummits the four angles 



G, 



