24 NEW YORK STATE MUSEUM 
manner two of which are shown in figures 9 and 10, the vertical lengths of 
these being respectively in ratio of } and 2 to the vertical axis of calcite. 
The rhombohedrons of this series stand in reversed relation to those of the 
positive series the faces of one corresponding to the terminal edges of the 
other; they are for this reason designated by the French crystallographers 
as rhomboedre inverse or in our system of nomenclature as negative rhombo- 
hedrons. As in the case of the series of positive rhombohedrons the limits of 
the series of negative rhombohedrons are the basal pinacoid and the prism 
of the first order. There have 
been recorded 54 negative 
rhombohedrons for calcite the 
flattest of which has a vertical 
length of 5 and the steepest a 
vertical length of 36 times the 
vertical ratio. Positive and 
negative rhombohedrons are 
so related that the terminal 
edges of any positive rhombo- 
hedron are truncated by the 
faces of a negative rhombo- 
Fig. 11 
hedron of + its vertical axial 
length or any negative rhombohedron is similarly modified in combination 
by a positive rhombohedron of } its vertical axial length. This relation is 
shown in figure 11 which is a combination of the rhombohedrons shown in 
figures 7, 9 and 10.1 
Scalenohedrons. Taking as a basis the fundamental rhombohedron, 
assume its vertical axis to be extended to 3, 2 and 3 times its vertical length 
and connect these points with the lateral angles of the rhombohedron by 
systems of lines as shown in figure 12. The three solids developed by this 
construction are each made up of 12 scalene triangles and have a common 
‘ For examples of the symmetry of rhombohedrons in combination compare plate 6, 
figure 5. 
