52 CRYSTALLOGRATHY. 



The twelve-sided double pyramid lias in each pyramid a pail 

 of faces for each sector ; that is, six pairs for each pyramid. If 

 now the three alternate of these pairs, and those in the upper 

 pyramid alternate with those of the lower (the shaded in fig. 23) f 

 were enlarged to the obliteration of the rest of the planes, the 

 resulting form would be a scalenohedron — a 

 solid with three pairs of planes to each pyra- 

 mid instead of six. Such is the mathematical 

 relation of the scalenohedron to the twelve- 

 sided double pyramid. If the faces enlarged 

 were those not shaded in fig. 23, another 

 scalenohedron would be obtained which would 

 be the minus scalenohedron, if the other were 

 designated the^Zws. 



Fig. 8 shows the relations of a rhombohe- 

 dron to a hexagonal prism. The planes H 

 replace three of the terminal edges at each base of the prism, 

 and those above alternate with those below. The extension 

 of the planes Ji to the obliteration of those of the prismatic 

 planes, I, and that of the basal plane O, would produce the 

 rhombohedron cf fig. 1. Figs. 9 and 10 represent the same 

 prism, but with terminations made by the rhombohedron of fig. 2. 

 By comparing the above figures, and noting that the planes 

 of similar forms are lettered alike, the combinations in the 

 figures will be understood. Fig. 16 is a combination of the 

 planes of the fundamental rhombohedron R, with those of an- 

 other rhombohedron 4, and of two scalenohedrons l 3 and 1\ 

 Fig. 17 contains the planes of the rhombohedron — -£, with those 

 of the scalenohedron V and those of the prism i. These figures, 

 and figs. 14, 22, ha\e the fundamental rhombohedron revolved 

 60° from the position in fig. 1, so that two planes H are in view 

 above instead of the one in that figure. 



2. Lettering of Figures.— Figs. 1 to (5, representing rhombohe- 

 Irons of the species calcite, are lettered with numerals, excepting fig. 1, 

 la fig. 1 the letter R stands for the numeral 1, and the numerals on the 

 others represent the relative lengths of their vertical axes, the lateral 

 b*.ing equal. In fig. 4 the vertical axis is twice that in fig. 1 ; in fig. (5 

 thirteen times ; and in fig. 15 the planes lettered 16 are those of a rhom- 

 bohedron whose vertical axis is sixteen times that of fig. 1. The rhom- 

 Nmedrons of figs. 1, 5, 6, and 15 Axe plus rhombohedrons ; that is, they 

 *re in the same vertical series ; while 2 and 3 are minus rhombohe- 

 drons, as explained above. The rhombohedron, when its vertical axia 

 is reduced in length to zero, becomes the single basal plane lettered 

 in the series. If, on the contrary, the vertical axis of the rfc.ombohe- 

 (boti is lengthened to infinity, the faces of the rhombohedron become 



