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own form of crystal, a science, or branch of mineralogy, has arisen,
called "crystallography," and out of the conglomeration of confused
forms there have been evolved certain rules of comparison by which all
known crystals may be classed in certain groups.

This is not so laborious a matter as would appear, for if we take a
substance which crystallises in a cube we find it is possible to draw
nine symmetrical planes, these being called "planes of symmetry," the
intersections of one or more of which planes being called "axes of
symmetry." So that in the nine planes of symmetry of the cube we get
three axes, each running through to the opposite side of the cube. One
will be through the centre of a face to the opposite face; a second will
be through the centre of one edge diagonally; the third will be found in
a line running diagonally from one point to its opposite. On turning the
cube on these three axes--as, for example, a long needle running through
a cube of soap--we shall find that four of the six identical faces of
the cube are exposed to view during each revolution of the cube on the
needle or axis.

These faces are not necessarily, or always, planes, or flat, strictly
speaking, but are often more or less curved, according to the shape of
the crystal, taking certain characteristic forms, such as the square,
various forms of triangles, the rectangle, etc., and though the crystals
may be a combination of several forms, all the faces of any particular
form are similar.

All the crystals at present known exhibit differences in their planes,
axes and lines of symmetry, and on careful comparison many of them are
found to have some features in common; so that when they are sorted out
it is seen that they are capable of being classified into thirty-three
groups. Many of these groups are analogous, so that on analysing them
still further we find that all the known crystals may be classed in six
separate systems according to their planes of symmetry, and all stones
of the same class, no matter what their variety or complexity may be,
show forms of the same group. Beginning with the highest, we have--(1)
the cubic system, with nine planes of symmetry; (2) the hexagonal, with
seven planes; (3) the tetragonal, with five planes; (4) the rhombic,
with three planes; (5) the monoclinic, with one plane; (6) the
triclinic, with no plane of symmetry at all.

In the first, the cubic--called also the isometric, monometric, or
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