20 NEW YORK STATE MUSEUM 
MATHEMATICAL RELATIONS AND FORMULAS 
General types of forms. The fundamental form of calcite and conse- 
quently the one which is used as a basis in all systems of symbol nomen- 
clature is the primary rhombohedron, familiar as the cleavage form. Assum- 
ing the ideal development of this form shown in figure 1,' it will be seen 
to be bounded by six similar rhombic faces which 
intersect in six equal lateral edges forming a zigzag 
line around the crystal, and six equal terminal 
edges, three of which form the upper and three, in 
alternate position the lower terminal solid angle. 
By joining the middle points of the opposite 
lateral edges by three intersecting lines and the 
terminal angles by a fourth, we get the system of 
dotted lines shown in the figure. Considering 
figure 1 in vertical projection or “plan” [fig. 2] two 
facts are to be noted. 
1 The vertical dotted line is an axis of trigonal 
symmetry or threefold symmetry. 
2 The three dotted lines joining the lateral 
Fig. 1 
edges are equal, equally inclined and lie in a plane 
perpendicular to the vertical dotted line. These four lines constitute the 
crystallographic axes of the hexagonal system. The ratio of the length 
of the vertical axis to each of the horizontal or basal axes, for calcite is 
represented by the proportion .8543:1, this ratio being determined by the 
unit form which is the cleavage rhombohedron. 
Base. If now, a pair of planes be assumed normal to the vertical axis, 
they will truncate the terminal solid angles as shown in figure 3, producing 
1Tn this as in all other pictorial projections unless otherwise stated the crystal is 
shown in clinographic parallel perspective, that is the crystal is assumed to be revolved 
18° 26’ to the right, and the upper termination is inclined 9° 28’ to the front of the plane 
of vision. 
