MINERALOGY. 49 
same mineral. Thus iron pyrites or sulphuret of iron occurs in cubes, 
octahedrons, pentagonal dodecahedrons, rhombic dodecahedrons : frequently 
in the same crystal we may have faces of all these different forms. 
Il. The Dimetric System, Dana. Das viergliederige System, Weiss. 
Pyramidal, Mohs. Tetragonal, Naumann. Monodimetric, Hausmann. 
The fundamental form of this system is an octahedron with a longer or 
shorter vertical axis and two equal lateral axes (the three axes all at right 
angles to each other). 
1. The Square Octahedron. It is called obtuse (fig. 32) when the 
vertical axis is shorter than the other, and acute (fig. 33) when longer. 
The figures of the derivative forms are based on these proportions of the 
primary axes. As the vertical axis is always unequal in respect to two 
equal lateral axes, there will be different values in the derivatives. Thus 
the two corners through which the primary axis passes (pl. 32, fig. 34) 
may be truncated without the four corners of the secondary axes requiring 
a similar truncation. Elongations and contractions may occur in the 
direction of the primary axis, while the two secondaries mutually retain an 
equality of length. 
The acute, like the obtuse octahedron, has the same number of faces, 
edges, and corners, or solid angles, as the regular; the base is in all a 
square; the side triangles, however, bounding the solid, are in the former 
isosceles, in the latter equilateral. The derivative forms from the square 
octahedron are, the octahedron (fig. 39) with truncated lateral edges: 
fig. 38 with truncated, and fig. 46 with bevelled basal edges. Also the 
octahedron with the corners of the vertical axis replaced by four plane 
faces (fig. 49). 
2. The Right Square Prism (fig. 35). It is produced by truncating the 
four basal edges of the octahedron, as also the extremities of the vertical 
axis. The figure is bounded by four equal lateral rectangles and two 
terminal squares. fig. 37 represents the right square prism, with its 
corners truncated until the terminal faces are replaced, each by a solid 
angle. 
3. The Regular Hight-sided Prism ( fig. 36) is obtained by bevelling the 
vertical edges of the right square prism. The double eight-sided pyramid 
( jig. 40) is produced by cutting off the basal edges of the eight-sided right 
prism (fig. 36), by planes meeting at the extremities of the vertical axis, 
and obliterating the lateral faces. 
4. The Twelve-sided Prism ( fig. 41) is produced by bevelling the vertical 
edges of the right square prism, without obliterating the lateral faces, as in 
the regular eight-sided prism. 
5. The Square Plate, with Four Bevelled Edges ( fig. 82), is produced by 
truncating the extremities of the square octahedron. 
III. The Trimetric System, Dana. Das zwei-und-zweigliederige System, 
Weiss. Orthotype, Mohs. Rhombic, Naumann. Holohedral-rhomoic, 
Breithaupt. 
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