59 ORYSTALLOGRAPHY. 
The twelve-sided double pyramid has in each pyramid a pair 
of faces for each sector; that is, six pairs foreach 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), 
were enlarged to the obliteration of the rest of the planes, the 
29. 
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 plus. 
Fig. 8 shows the relations of a rhombohe- 
dron to a hexagonal prism. The planes & 
replace three of the terminal edges at each base of the prism, 
and those above alternate with those below. The extension 
of the planes # to the obliteration of those of the prismatic 
planes, Z, 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 rhombobedron 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 /?, with those of an- 
other rhombohedren 4, and of two scalenohedrons 1° and 1?. 
Fig. 17 contains the planes of the rhombohedron —4, with those 
of the scalenohedron 1|*, and those of the prism 7. ‘These figures, 
and figs. 14, 22, have the fundamental rhombohedron revolved 
60° from the position in fig. 1, so that two planes & are in view 
above instead of the one in that figure. 

2. Lettering of Figures.—Figs. 1 to 6, representing rhombohe- 
drons of the species calcite, are lettered with numerals, excepting fig. 1, 
In fig. 1 the letter # stands for the numeral 1, aud the numerals on the 
others represent the relative lengths of their vertical axes, the latecal 
being equal. In fig. 4 the vertical axis is twice that in fig. 1; in fig. 6 
thirteen times; and in fig. 15 the planes lettered 16 are those of a rhom- 
tvohedron whose vertical axis is sixteen times that of fig. 1. The rhom- 
hwohedrons of figs. 1, 5, 6, and 15 are plus rhombohedrons; that is, they 
sre in the same vertical series; while 2 and 38 are minus rhombohe- 
drons, as explained above. The rhombohedron, when its vertical axis 
is reduced in length to zero, becomes the single basal plane lettered O 
in the series.. If, on the contrary, the vertical axis of the rhombohe- 
iron is lengthened to infinity, the faces of the rhombohedron become 
