2 
The position of the planes gives rise to the following 
distinctions :— Terminal or basal planes occur only in such 
crystals as have a greater or smaller extension in one or 
two directions ; the same remark applies to the lateral 
planes which unite the terminal planes, and form the sides 
of the crystal when it is viewed in an upright position. 
Those planes of composite crystals which end in a terminal 
angle or edge are called vertical planes. Original or 
primary planes are those which belong to the primary 
form of a body; secondary planes, or planes of combina¬ 
tion, are those which exist in derived forms, such as are 
produced by truncation of the edges, angles, etc. Thus, 
for example, in Fig. 8, Plate B, the cube is the primary 
form, and its planes are marked P. The planes lying on 
the edges, D, are secondary planes, whose origin is the 
even truncation of the edges. Now, as the cube has 
twelve edges, and as these secondary planes are subject to 
the law of symmetry, it follows that all the edges of the 
same kind must be truncated. In Fig. 7, the primary 
form, a regular octahedron, is changed, its angles being so 
truncated that the cube predominates ; the planes of the 
octahedron are marked 0, those of the cube P. If the 
planes of the cube be again increased, the planes of the 
octahedron will entirely disappear, and the derived form 
of the cube will have completely replaced the primary 
form of the octahedron. This is frequently exemplified so 
far in the case of fluor spar. Fig. 9 represents an example 
of oblique disposition of the secondary planes, and Fig. 10 
gives another of double truncation or sharpening of the 
angles of the cube. 
Edges are the right lines in which two planes meet. 
A solid, with all its edges alike, is called single or equal- 
edged, as in Plate B, Fig. 2 ; with two kinds of edges (Fig. 
12), is said to be double-edged, and so on. In Fig. 12, those 
edges which lie between the basal and lateral planes are 
called basal edges, those between the lateral planes are 
called lateral edges. In Fig. 5, the three edges converg¬ 
ing in the terminal angle are called the vertical edges, 
those running vertically, the lateral edges, and those 
between the terminal and lateral planes, the basal edges. 
According to the direction in which two planes meet in an 
edge, edges are distinguished as acute , obtuse , and rectan¬ 
gular, the angle of direction being ascertained by means 
of an instrument called the goniometer. 
Angles are the points in which three or more edges 
meet. According to the position we distinguish terminal 
angles, basal angles, afld so on. For example, in Fig. 3, 
Plate B, the upper and under ones are terminal or vertical 
angles, the four others united by the basal edges are called 
basal angles. 
Axes. —Those right lines are called axes, which in 
imagination so pass through the centre of a crystal, that 
its planes, edges, and angles, are grouped in equal masses 
around it. In many bodies there are three, and in a 
smaller number four axes admitted as giving measurements. 
All the essential peculiarities of crystals depend upon the 
length and position of these axes. The systematic classi¬ 
fication of all crystals has therefore been founded on the 
relations of their axes, as given below. 
I. Monometric or Tesseral Solids, with three equal axes 
intersecting each other at right angles. To this 
system belong— 
a. Simple elementary forms. 
1. The Cube, hexahedron, or quadratic 
hexahedron. Plate A, Fig. 2. 
2. The regular Octahedron. Plate A, 
Fig. 14. 
3. The Rhombic Dodecahedron, or grana- 
toid. Plate A, Fig. 4. 
b. Hemihedral forms. 
4. The Tetrahedron, or hemi-octahedron. 
Plate XV., Fig. 17. 
5. The Pentagonal Dodecahedron, or pyri- 
toid. Plate A, Fig. 20. 
c. Derived Crystals. 
6. The Leucitoid, or Trapezohedron. Plate 
A, Fig. 12. 
7. The Parallel, or Pyritohedral Hemi-hex- 
octahedron. Plate A, Fig. 10. 
8. The Trigonal Trisoctahedron. Plate I., 
Fig. 2. 
9. The Pyramidal Cube. Plate X., Fig. 17. 
10. The Icosahedron. Plate XVII., Fig. 8. 
11. The Hexoctahedron. Plate B, Fig. 1. 
This system further includes all modified forms of the 
primary solids above mentioned, such as are produced by 
truncation of the edges and angles. For example, the 
cubo-octahedron, Plate B, Fig. 7 ; the cubo-dodecahedron, 
Fig. 8 ; the cubo-pentagonal dodecahedron, Fig. 9 ; the 
cubo-leucitoid, Fig. 10 ; the double tetrahedron, Plate XV., 
Fig. 18; the pyramidal tetrahedron, Plate XXI., Fig. 6, 
and so on. 
II. Dimetric Solids, with a vertical axis longer or shorter 
than the two equal transverse axes, which are 
perpendicular to one another, and to the vertical 
axis. This system includes the following forms :— 
1. The Square Octahedron. Plate B, Fig. 3. 
2. The Right Square Prism. Plate B, Fig. 12. 
And of derived forms, the hemihedral square 
octahedron. 
III. Trimetric Solids, with three unequal axes intersecting 
each other at right angles— 
1. The Rhombic Octahedron, figured in Plate 
XII., Fig. 1, with truncation of the vertical 
and upper basal edges. 
2. The Right Rhombic Prism. Plate B, Fig. 13. 
3. The Right Rectangular Prism, Plate A, Fig. 
6, and the rectangular octahedron derived 
therefrom. 
IV. Monoclinic Solids. All the axes are unequal, two of 
them are perpendicular to one another, the third 
forms with one of these an oblique angle. Phis 
system includes— 
1. The Oblique Rhombic Prism. Plate B, Fig. 14. 
2. The Oblique Rectangular Prism, Plate X., 
Fig. 7, and the oblique rhombic, and oblique 
rectangular octahedrons derived from these. 
V. Triclinic Solids, with three unequal and oblique axes. 
This system includes— 
The Oblique Rhomboidal Prism, Plate B, Fig. 15, 
with its combinations. 
