RHOMBOHEDRAL SECTION OF HEXAGONAL SYSTEM. 54 
rhombohedron, and they are at right angles to the vertical axis. 
lt is stated on page 45 that rhombohedral forms are, from a 
mathematical point of view, hemihedral under the hexagonal 
system. The rhombchedron, which may be considered a double 
three-sided pyramid, is hemihedral to the double six-sided pyra- 
mid. Fig. 19, representing the latter form, has its altcrnate 
faces shaded ; suppressing the faces shaded the form would be 
that of fig. 18; and suppressing, instead of these, the faces not 
shaded, the form would be that of another rhombohedron, dif- 
fering only in position. The two are distinguished as plus and 
metus rhombohedrons. They are combined in figs. 20, 21, 
_ forms of quartz. Rhombohedrons vary greatly in the length of 
the vertical axis with reference to the lateral. Figs. 1, 2, 3, and 
18 represent crystals with the vertical axis short, and figs. 4, 5, 
6 others with a long vertical axis. In the former the terminal 
edges are obtuse and the lateral acute, and the latter have the 
terminal edges acute and the lateral obtuse; the former are 
called obtuse rhombohedrons, and the latter acute. 
The cube placed on one solid angle, with the diagonal between 
it and the opposite solid angle vertical, is, in fact, a rhembohe 
dron intermediate between obtuse and acute rhombohedrous— 
the edges that are the terminal in this position, and those that 
are the lateral, being alike rectangular edges. Fig. 3 has nearly 
the form of a cube in this position. 
The relation of one series of scalenohedrons to the rhvs.bo 
hedron is illustrated in fig. 22. This figure 
represents a rhombohedron with the lateral 
edges bevelled. These bevelling planes are 
those of a scalenohedron, and the outer lines 
of the same figure show the form of that 
scalenohedron which is obtained when the 
bevelment is continued to the obliteration 
of the rhombohedral planes. Fig. 14 repre- 
sents this scalenohedron with the rhombohe- 
dral planes much reduced in size. Other 
scalenohedrons result when the terminal 
edges are beveiled, and still others from 
pairs of planes on the angles of a rhombolie- 
dron. 
The scalenohedron is hemihedral to the 
twe've-sided double pyramid (fig. 23). 
In the hexagonal system the three verti- ads 
cal axial planes divide the space about the yl 
vertical axis into six sectors (fig. 12, p. 48). 


