in Chemical Combinations. 189 



in the plans which pass by the centre of the cube, and by the 

 tliree sides of tliis cube which form the solid angle. The thirty- 

 two summits of the eight tetrahedrons arranged in this way will 

 be those of a polyhedron, which, in the case vvhere the tetrahe- 

 droiis are regular and have their centre of gravity at the same 

 point, will have eighteen faces; viz. six square and twelve hexa- 

 gonal. 



It is easy to see that this polyhedron is nothing but a dode- 

 cahedron, of which the six summits with four faces shall have 

 been curtailed by one-third of the adjoining ridges ; as the po- 

 sition of the eight tetrahedrons of which it is composed is the 

 same for all, I have given it the name of octo-tetrahedron. The 

 eight tetrahedrons which form this polyhedron by their junction, 

 are placed tv/o and two like the two tetrahedrons which form a 

 cube, and four and four like the four tetrahedrons of which the 

 tetra-tetrahedron is composed ; we may therefore consider it 

 also as produced by the union of four cubes, or of two tetra- 

 tetrahedrons. 



The octo-tetrahedron having six faces, the middle parts of 

 which are situated respectively like the "six summits of an octo- 

 hedron, we shall be able to unite these two polyhedrons into one 

 only, in a manner analogous to that in wliich tlie combinations 

 hitherto described are formed : but as this polvhedron is less 

 simple than the amphihedron, which contains precisely as many 

 tetrahedrons and octohedrous, and which conseciuently neces • 

 sarily leads to the same results, relative to the combinations of 

 bodies in determinate proportions ; I shall not reckon it among 

 the representative forms. 



It is evident that the octo-tetrahedron, which has eight sum- 

 mits situated with respect to each other like the eight summits 

 of a cube, cannot be combined with this form ; but it may, like 

 the hexa-tetrahedron, be combined with a hex^hedral prism, 

 because it partakes with the hexa-tetrahedron of the property 

 of having hexagonal faces. In order to form a clear idea of 

 this combination, we may conceive a line which joins the mid- 

 dles of the two opposite hexagonal faces of an octo-tetrahedron, 

 and place it in a vertical situation ; we then find that those two 

 f;ices are each surrounded by six other faces, viz. two square 

 and four hexagon ; and that we may place a hexagonal prism in 

 such a way as that, the six summits of each of its bases answer- 

 ing to those six faces, its axis will be confounded with the line 

 situated vertically. 



The two polyhedrons thus joined give a representative form, 

 which differs only from the octo-tetrahedron inasmuch as the 

 twelve faces of the latter, which surround the two bases, are 

 < uverc (1 by as many pyramids, four quadrangular and eight hexa- 

 gonal. 



