MINERALOGY. 51 
The axes by which we measure the dimensions of this system are two 
lateral, unequal, crossing each other at a right angle, and a third oblique 
to one of the lateral, but at right angles with the other. Considering an 
octahedron as belonging to this system, its upper and lower faces would be 
different. It is customary to consider an oblique rhombic prism as the 
primary form, whose extremities stand perpendicularly to the lateral edges, 
and at an oblique angle with reference to the other two. From this prism 
the other forms may be derived as before. PJ. 32, figs. 59 and 60, 
represent two prisms in which two edges are truncated by the face a, 
producing oblique six-sided prisms. fig. 61 represents an octahedron with 
half the edges truncated. ig. 62 is a prism corresponding to the case in 
which half the basal edges are truncated. 
V. The Triclinic System, Dana. Das Ein-und-eingliederige System, 
Weiss. Anorthotype, Mohs. Triclinohedral, Naumann. 
An oblique rhomboidal prism is the basis of this system. All three axes 
are here oblique and unequal. A prism of this character is shown in 
jigs. 64 and 65. In this system only two parallel faces and two opposite 
edges are of like value. For this reason we see the truncation of the edges 
extended only to two diagonally opposite edges, as in fig. 63. The 
inclination of the plane which truncates these edges is different with respect 
to one face of the edge from the other; and the six-sided prism (fig. 66) 1s 
consequently irregular. 
VI. The Hexagonal System. Das Sechsgliederige System, Weiss. 
Rhombohedral, Mohs. Hexagonal, Naumann, Dana. Monotrimetric, 
Hausmann. 
This system exhibits a striking peculiarity, as compared with the others. 
While, in the preceding systems, the dimensions of bodies were given in the 
least number of axes (namely, three) in which their exteriors could be 
considered; the simplest conditions are obtained by assuming four axes. 
Three of them lie in one plane, and having equal inclination to each other, 
are of equal length: they thus form the diagonals of a regular hexagon. 
The fourth, assumed as the vertical axis, is unequal to the three others, and 
stands perpendicular to their plane. As the primary form of this system 
we may assume the double six-sided pyramid (figs. 67 and 73). This is a 
solid bounded by twelve isosceles triangles. Truncating the basal edges by 
planes parallel to the vertical axes, will give us the pyramidal six-sided 
prism (fig. 68). Truncating the terminal solid angles of fig. 68 will give 
us the regular six-sided prism, with right terminal faces ( figs. 70 and 71). 
Fig. 72 is obtained by truncating the corners of fig. 70; bevelling the 
six vertical edges we have the twelve-sided prism (fig. 42); and by 
bevelling four edges the prism (fig. 76). A form of this system, occurring 
frequently in calcareous spar, is the scalene octahedron (jig. 74). The 
hemihedral shape of the double six-sided pyramid, or the rhombohedron 
(pl. 32, fig. 75), is often assumed as the primary form of this system. One 
and the same crystal is thus frequently inclosed by faces of several 
ICONOGRAPHIC ENCYCLOP ZDIA.—VOL. I. 31 481 
