RHOMBOHEDEAL SECTION OF HEXAGONAL SYSTEM. 51 



rhombohedron, and they are at right angles to the vertical axis. 

 It is stated on page 45 that rhombohedral forms are, from a 

 mathematical point of view, hemikedral under the hexagonal 

 system. The rhombohedron, which may be considered a double 

 three-sided pyramid, is hemihedial to the double six-sided pyra- 

 mid. Fig. 19, representing the latter form, has its altcrna+e 

 faces shaded ; suppressing the faces shaded the form would Le 

 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 

 minus rhombohedrons. They are combined in figs. 20, 21, 

 forms of quartz. .Rhombohedrons vaiy 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 

 sdges 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 rhombohe- 

 dron intermediate between obtuse and acute rhombohedrons — 

 the edges that are the terminal in this position, and those thai 

 are the lateral, being alike rectangular edges. Fig. 3 has nearlj 

 the form of a cube in this position. 



The relation of one series of scalenohedrons to the rhr-a'AK) 

 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 bevelled, and still others from 

 pairs of planes on the angles of a rhombohe- 

 dron. 



The scalenohedron is hemihedral to the 

 tweVe-sided double pyramid (tig. 23). 



Jn the hexagonal system the three verti- 

 cal axial planes divide the space about the 

 vertical axis into six sectors (fig. 12, p. 48). 



